Keywords: Randomized methods
Abstract: Clamping force control in Electro Mechanical Brakes (EMBs) is a challenging task, mainly due to the nonlinear dynamics of the system and the uncertainty affecting its physical parameters. In this paper, a robust tuning of a PID control loop for an EMB is proposed. First, a control-relevant linear model of the system is derived. Then, the optimal parameters of the controller are tuned by solving a convex pole-placement problem and probabilistic robustness guarantees are provided according to the scenario theory. Finally, the performance of the proposed strategy is assessed on a complex nonlinear simulator of the EMB dynamics, and compared with the state of the art approach for robust control of EMBs.

Keywords: Learning for control
Abstract: We consider the problem of discounted optimal state-feedback regulation for general unknown deterministic discrete-time systems. It is well known that open-loop instability of systems, non-quadratic cost functions and complex nonlinear dynamics, as well as the on-policy behavior of many reinforcement learning (RL) algorithms, make the design of model-free optimal adaptive controllers a challenging task. We depart from commonly used least-squares and neural network approximation methods in conventional model-free control theory, and propose a novel family of data-driven optimization algorithms based on linear programming, off-policy Q-learning and randomized experience replay. We develop both policy iteration (PI) and value iteration (VI) methods to compute an approximate optimal feedback controller with high precision and without the knowledge of a system model and stage cost function. Simulation studies confirm the effectiveness of the proposed methods.

Keywords: Multi-agent systems, Stochastic control and game theory, Learning for control
Abstract: We study a general class of repeated auctions, such as the ones found in electricity markets, as multi-agent games between the bidders. In such a repeated setting, bidders can adapt their strategies online using no-regret algorithms based on the data observed in the previous auction rounds. Well-studied no-regret algorithms depend on the feedback information available at every round, and can be mainly distinguished as bandit (or payoff-based), and full-information. However, the information structure found in auctions lies in between these two models, since participants can often obtain partial observations of their utilities under different strategies. To this end, we modify existing bandit algorithms to exploit such additional information. Specifically, we utilize the feedback information that bidders can obtain when their bids are not accepted, and build a more accurate estimator of the utility vector. This results in improved regret guarantees compared to standard bandit algorithms. Moreover, we propose a heuristic method for auction settings where the proposed algorithm is not directly applicable. Finally, we demonstrate our findings on case studies based on realistic electricity market models.

Keywords: Multi-agent systems, Randomized methods, Learning for control
Abstract: In this paper, we consider optimization problems involving multiple agents. Each agent introduces its own constraints on the optimization vector, and the constraints of all agents depend on a common source of uncertainty. We suppose that uncertainty is known locally to each agent through a private set of data (multi-agent scenarios), and that each agent enforces its scenario-based constraints to the solution of the multi-agent optimization problem. Our goal is to assess the feasibility properties of the corresponding multi-agent scenario solution. In particular, we are able to provide a priori certificates that the solution is feasible for a new occurrence of the global uncertainty with a probability that depends on the size of the datasets and the desired confidence level. The recently introduced wait-and-judge approach to scenario optimization and the notion of support rank are used for this purpose. Notably, decision-coupled and constrained-coupled uncertain optimization programs for multi-agent systems fit our framework and, hence, any distributed optimization scheme to solve the associated multi-agent scenario problem can be accompanied with our a priori probabilistic feasibility certificates.

Keywords: Dynamic Networks
Abstract: Dynamic Networks are signal flow graphs explicitly partitioning structural information from dynamic or behavioral information in a dynamic system. This paper develops the mathematical foundations underlying this class of models, revealing structural roots for system concepts such as system behavior, well-posedness, causality, controllability, observability, minimality, abstraction, and realization. This theory of abstractions uses graph theory to systematically and rigorously relate LTI state space theory, developed by Kalman and emphasizing differential equations and linear algebra, to the operator theory of Weiner, emphasizing complex analysis, and Willem’s behavioral theory. New systems concepts, such as net effect, complete abstraction, and extraneous realization, are introduced, and we reveal conditions when acyclic abstractions exist for a given network, opening questions about their use in network reconstruction and other applications.

Keywords: Dynamic Networks, Machine learning, Recursive identification
Abstract: Synchronized phasor measurements in power transmission and distribution networks enable real-time monitoring of voltage and currents. Such measurements can be used to monitor power flow, but also to monitor important electric parameters of the network. In this paper, it is shown how synchrophasor measurements can be used for real-time monitoring of the admittance of the connections between buses in a power network, typically the three-phase transmission or distribution lines. The objective is to formulate admittance monitoring capabilities in which changes in three-phase line admittance can be monitored in real-time and achieved by the formulation of synchrophasor-based recursive estimation techniques over short time intervals.

Keywords: Dynamic Networks, Identifiability, Input and excitation design
Abstract: For identifiability of a single module in a dynamic network, excitation signals need to be allocated at particular nodes in the network. Current techniques provide analysis tools for verifying identifiability in a given situation, but hardly address the synthesis question: where to allocate the excitation signals to achieve generic identifiability. Starting from the graph topology of the considered network model set, a new analytic result for generic identifiability of a single module is derived based on the concept of disconnecting sets. For the situation that all node signals are measured, the vertices in a particular disconnecting set provide the potential locations to allocate the excitation signals. Synthesis approaches are then developed to allocate excitation signals to guarantee generic identifiability.

Keywords: Dynamic Networks
Abstract: Identification of dynamic networks has been a flourishing area in recent years. However, there are few contributions addressing the problem of simultaneously identifying all modules in a network of given structure. In principle the prediction error method can handle such problems but this methods suffers from well known issues with local minima and how to find initial parameter values. Weighted Null-Space Fitting is a multi-step least-squares method and in this contribution we extend this method to rational linear dynamic networks of arbitrary topology with modules subject to white noise disturbances. We show that WNSF reaches the performance of PEM initialized at the true parameter values for a fairly complex network, suggesting consistency and asymptotic efficiency of the proposed method.

Keywords: Dynamic Networks, Identifiability, Closed loop identification
Abstract: Over the last decade, the problem of data-driven modeling in linear dynamic networks has been introduced in the literature, and has shown to contain many different challenging research questions, that go far beyond the classical problems in open-loop and closed-loop identification. The structural and topological properties of networks become a central ingredient in the related identification setting, as well as the selection of locations for signals to be sensed and for excitation signals to be added. In this seminar we will present an overview of recent results that are obtained for the problem of identification of a single link/module in a dynamic network of which the topology is given. The surveyed methods include extensions of the direct and indirect methods of closed-loop identification, as well as Wiener filter approaches and Bayesian kernel-based methods. Particular attention will be given to the selection of signals that need to be available for measurement/excitation, and accuracy properties of the estimated models in terms of consistency and minimum variance properties.

Keywords: Distributed control and estimation, Learning for control
Abstract: The paper presents data-driven algorithms to estimate in a distributed manner the eigenvalues, right and left eigenvectors of an unknown linear (or linearized) interconnected dynamic system. In particular, the proposed algorithms do not require the identification of the system model in advance before performing the estimation. As a first step, we consider interconnected dynamical system with distinct eigenvalues. The proposed strategy first estimates the eigenvalues using the well-known Prony method. The right and left eigenvectors are then estimated by solving distributively a set of linear equations. One important feature of the proposed algorithms is that the topology of communication network used to perform the distributed estimation can be chosen arbitrarily, given that it is connected, and is also independent of the structure or sparsity of the system (state) matrix. The proposed distributed algorithms are demonstrated via a numerical example.

Keywords: Learning for control
Abstract: For linear time-invariant systems having a state matrix with uncertain sign, we formulate and solve a minimax adaptive control problem as a zero sum dynamic game. Explicit expressions for the optimal value function and the optimal control law are given in terms of a Riccati equation. The optimal control law is adaptive in the sense that past data is used to estimate the uncertain sign for prediction of future dynamics. Once the sign has been estimated, the controller behaves like standard H-infinity optimal state feedback.

Keywords: Dynamic Networks
Abstract: The paper considers the problem of inferring individual network edges from time-series data. This is the problem faced in target identification, but also important in cases where it is of interest to learn whether two specific network nodes interact directly as well as in cases where there is insufficient information to infer the full network. The proposed inference method is based on taking a geometric perspective on a corresponding regression problem. We show that, by considering the span of individual node response vectors in sample space, it is possible to identify a given edge with a label of confidence even if the available data are not informative to infer other parts of the network. Furthermore, the method points to what further experiments are needed to infer edges for which the available response data are not sufficiently informative. We demonstrate the results on a target identification problem of a nonlinear 20-gene network and show that targets can be identified independently from a single time-series experiment using significantly fewer samples than the number of nodes in the network.

Keywords: Bayesian methods, Experiment design, Grey box modelling
Abstract: We consider systems under uncertainty whose dynamics are partially unknown. Our aim is to study satisfaction of temporal properties by trajectories of such systems. We express these properties as signal temporal logic formulas and check if the probability of satisfying the property is at least a given threshold. Since the dynamics are parameterized and partially unknown, we collect data from the system and employ Bayesian inference techniques to associate a confidence value to the satisfaction of the property. The main novelty of our approach is to combine both data-driven and model-based techniques in order to have a two-layer probabilistic reasoning over the behavior of the system: one layer is related to the stochastic noise inside the system and the next layer is related to the noisy data collected from the system. We provide approximate algorithms for computing the confidence for linear dynamical systems.

Keywords: Dynamic Networks
Abstract: We address the issue of estimating the topology and dynamics of sparse linear dynamic networks in a hyperparameter-free setting. We propose a method to estimate the network dynamics in a computationally efficient and parameter tuning-free iterative framework known as SPICE (Sparse Iterative Covariance Estimation). Our approach does not assume that the network is undirected and is applicable even with varying noise levels across the modules of the network. We also do not assume any explicit prior knowledge on the network dynamics. Numerical experiments with realistic dynamic networks illustrate the usefulness of our method.

Keywords: Dynamic Networks, Time series modelling, Closed loop identification
Abstract: A challenge in neuroscience and many other fields of research is the inference of a network's structure from observations of dynamics on the network. Understanding the relationship between network structure and dynamics on a network can help improve methods for network inference. We consider ``process motifs'' on a network as building blocks of processes on networks and propose to distinguish process motifs and graphlets as two different types of network motifs. We demonstrate that the analysis of process motifs can yield insights into the mechanisms by which processes and network structure contribute to differential entropy and other information-based properties of stochastic processes on networks, and we discuss the relationship between process motifs and graphlets.

Keywords: Frequency domain identification, Subspace methods, Closed loop identification
Abstract: Difficult-to-obtain variables in industrial applications have led to the rise of soft sensors, which use prior system information and measurements to estimate these difficult-to-obtain variables. In real systems, the measurements that need to be estimated by a soft sensor are often infrequently measured or delayed. Sometimes, these delays and sampling time are variable in time. Though there are papers considering soft sensors in the presence of time delays and different sampling times, the variation of those parameters has not been considered when evaluating the adequacy of the soft sensors. Therefore, this paper will evaluate the impact of such variations for a data-driven soft sensor and propose modifications of the soft sensor that increase its robustness. The reliability of its estimate will be shown using the Bauer-Premaratne-Durán Theorem. Furthermore, the soft sensor will be simulated applying it to a continuous stirred tank reactor. Simulation showed that the modified soft sensor gives good estimates, whereas the traditional soft sensor gives an unstable estimate.

Keywords: Fault detection and diagnosis, Nonlinear system identification, Filtering and smoothing
Abstract: An online model-based fault detection and isolation method for salient permanent magnet synchronous motors is proposed using the parity-space approach. Given the polynomial model equations, Buchberger’s algorithm is used to eliminate the unknown variables (e.g. states, unmeasured inputs) resulting in analytic redundancy relations for residual generation. Furthermore, in order to obtain the derivatives of measured signals needed by such a residual generator, robust exact differentiators are used. The fault detection and isolation method is demonstrated using simulation of various fault scenarios for a speed controlled salient motor showing the effectiveness of the presented approach.

Keywords: Fault detection and diagnosis, Nonparametric methods, Machine learning
Abstract: In this paper, we propose the use of a change detection method to perform condition monitoring of mechanical components. The aim is to look for statistical changes in the distribution of features extracted from raw measurements, such as Root Mean Square or Crest Factor indicators. The proposed method works in a batch fashion, comparing data from one experiment to another. When these distributions differ by a specified amount, a degradation score is increased. The approach is tested on three experimental industrial applications: (i) an Electro-Mechanical Actuator (EMA) employed in flight applications, where the focus of the monitoring is on the ballscrew transmission; (ii) a CNC workbench, where the focus is on the vertical axe bearing, (iii) an industrial EMA with focus on the ballscrew bearing. All components undergone a severe experimental degradation process, that ultimately led to their failure. Results show how the proposed method is able to assess components degradation prior to their failure.

Keywords: Fault detection and diagnosis
Abstract: Process monitoring plays an important role in maintaining favorable process operation conditions and is gaining increasing attention in both academic community and industrial applications. This paper proposes a data-driven model predictive fault detection method to achieve efficient monitoring of dynamic processes. First, a measurement sample is projected into a dominant latent variable subspace that captures main variance of the process data and a residual subspace. Then the dominant latent variable subspace is further decomposed as a dynamic feature subspace and a static feature subspace. A fault detection residual is generated in each subspace, and corresponding monitoring statistic is established. By using the model predictive monitoring scheme, not only the status of a process but also the type of a detected fault, namely a dynamic feature fault or a static feature fault, can be identified. Effectiveness of the proposed data-driven model predictive monitoring scheme is tested on a lab-scale distillation process.

Keywords: Frequency domain identification, Identifiability, Closed loop identification
Abstract: As the amount of data stored from industrial processes increases with the demands of Industry 4.0, there is an increasing interest in finding uses for the stored data. However, before the data can be used its quality must be determined and appropriate regions extracted. Initially, such testing was done manually using graphs or basic rules, such as the value of a variable. With large data sets, such an approach will not work, since the amount of data to tested and the number of potential rules is too large. Therefore, there is a need for automated segmentation of the data set into different components. Such an approach has recently been proposed and tested using various types of industrial data. Although the industrial results are promising, there still remain many unanswered questions including how to handle a priori knowledge, over- or undersegmentation of the data set, and setting the appropriate thresholds for a given application. Solving these problems will provide a robust and reliable method for determining the data quality of a given data set.

Keywords: Fault detection and diagnosis, Distributed control and estimation
Abstract: The main objective of this paper is to develop an optimal distributed fault detection (FD) approach for large-scale systems in the presence of unknown deterministic disturbances using the measurement of sensor networks. To be specific, the design approach consists of two phases: the distributed offline training phase and the online implementation phase. The offline training phase includes distributed iterative learning and average consensus algorithm. It is worth mentioning that, the distributed approach avoids enormous computational costs and complex information exchanges. Finally, a numerical example is illustrated to show that the distributed approach can successfully and efficiently accomplish the FD task.

Keywords: Fault detection and diagnosis, Subspace methods
Abstract: Nowadays, many industrial processes generate large amounts of multimode data,which generally have a natural tensor structure, causing some faults invisible with traditional process monitoring (PM) and fault diagnosis (FD) methods. Tensor decomposition (TD) is a more practical approach for its effectiveness in solving high dimensionality problems as well as indicating the links between different modes. This paper proposes a common and individual feature extraction method based on TD, which identifies and separates the common and individual features from multimode data. The newly proposed approach is applied to a typical multimode hot strip mill process (HSMP), where common and individual feature for all steel products are existing. The final results indicate that the proposed approach can accurately detect and identify different faults in the HSMP.

Keywords: Fault detection and diagnosis, Nonlinear system identification, Identification for control
Abstract: As a data-driven process monitoring method, multivariable statistics techniques have special potentials and advantages to handle the increasingly prominent "Big data challenge" in the complex industrial systems. However, the standard partial least square (PLS) method and the principal component regression (PCR) method cannot maintain stable function in the nonlinear operating environment. In order to capture the precise relation of process variables and product variables, an approach called the revised kernel PCR (RKPCR) method is proposed in this thesis to resolve the problems encountered in the traditional PCR method. In addition, a brief and effective diagnosis logic is designed to decrease the difficulty of fault diagnosis. Finally, the effectiveness of the RKPCR algorithm is illustrated utilizing the Tennessee Eastman case (TEC) platform.

Keywords: Nonlinear system identification, Machine learning
Abstract: Data selection is a critical issue in data-driven soft sensor design. The paper proposes a new method for data selection based on a feature extraction step, followed by data selection algorithms. The method has been applied to an industrial case study, i.e., the estimation of the quality of processed wastewater produced by a Sour Water Stripping plant working in a refinery. The paper reports the results obtained with different data selection algorithms. The comparison has been performed both by using raw data and the feature extraction phase.

Keywords: Fault detection and diagnosis, Machine learning
Abstract: In this paper, a fault detection method of shipboard medium-voltage DC (MVDC) integrated electric propulsion system (IEPS) based on Ensemble Empirical Mode Decomposition (EEMD) and XGBoost is proposed. Particle swarm optimization (PSO) is used to optimize the parameters to solve the problem that the standard deviation of auxiliary white noise in EEMD needs to be artificially selected. Firstly, the voltage signal on the DC bus is preprocessed by PSO-EEMD, which is decomposed into a set of Intrinsic Mode Functions (IMFs) according to the local characteristic time scale of the signal, and then the energy entropy is calculated as the fault feature vector. The fault feature vector is used to train and test the fault classifier based on XGBoost, and finally the fault detection is completed. The simplified model of shipboard MVDC IEPS is built in AppSIM Time Simulator. The faults on generator output and DC cable are used to verify the proposed fault detection method. Fault feature extraction method and fault classifier design are completed in Python. Verification by simulation platform and comparison with other intelligent detection methods, it is proved that proposed detection method can detect different faults quickly and accurately, is enabled for future practical use.

Keywords: Time series modelling, Grey box modelling
Abstract: In industrial processes, causality analysis plays an important role in fault detection and topology building. Aiming to attenuate the influence of common correlation and noise, a feature based causality analysis method is proposed. By using the orthogonality and de-noising in feature analysis, it can capture more efficient causal factors. Moreover, better causal factors can make better predictions. Soft sensors based on least-squares regression and two neural networks are tested to compare the performance when using different causal factors and not using causal factors. The results show that the causal feature based soft sensors obtain the best performance and causal factors are crucial to prediction performance. Hence, it has great application potential owing to its strong interpretability and good accuracy.

Keywords: Estimation and filtering, Machine learning, Mechanical and aerospace estimation
Abstract: We propose a novel optimal estimation methodology for gasoline engine LP (low-pressure) EGR (exhaust gas recirculation) air-path system, which allows us to implement virtual sensors for oxygen mass fraction at the intake manifold and EGR mass flow rate at the LP-EGR valve, real sensors for them too expensive to deploy in production cars. We first decompose the LP-EGR air-path system into several sub-components; and opportunistically utilize physics-based modeling or data-driven modeling for each component depending on their model complexity. In particular, we apply the technique of MLP (multi-layer perceptron) as a means for data-driven modeling of LP-EGR/throttle valves and engine cylinder valve aspiration dynamics, all of which defy accurate physics-based modeling, that is also simple enough for real-time running. We further optimally combine these physics-based and data-driven modelings in the framework of UKF (unscented Kalman filtering), and also manifest via formal analysis that this mixed physics-based/data-driven modeling renders our estimator much faster to run as compared to the case of full data-driven MLP modeling. In doing so, we also extend the standard UKF theory to the more general case, where the system contains non-additive uncertainties both in the measurement and process models with cross-correlations and state-dependent variances, which stems from the inherent peculiar structure of our mixed physics-based/data-driven modeling approach, for the UKF formulation. Experiments are also performed to show the theory.

Keywords: Machine learning, Learning for control
Abstract: This paper presents a data-driven predictive control (DPC) algorithm for linear time-invariant (LTI) systems in the behavioral framework. The system is described by the parametrization of the Hankel matrix constructed from its measured trajectories. The proposed structure follows a two-step procedure. The existence of a controlled behavior is firstly verified from the perspective of dissipativity with the aid of quadratic difference forms (QdFs), then the controlled trajectory is selected from the original uncontrolled behavior through optimization. An illustrative example is presented to demonstrate the effectiveness of the proposed approach.

Keywords: Nonlinear system identification, Machine learning, Estimation and filtering
Abstract: Process complexities are characterized by strong nonlinearities, dynamics and uncertainties. Modeling such a complex process requires a flexible model with deep layers describing the corresponding strong nonlinear dynamic behavior. The proposed model is constructed by deep neural networks to represent the process of state transition and observation generation, both of which together constitute a stochastic nonlinear state space model. This model is evolved from the variational auto-encoder learned by the stochastic expectation-maximization algorithm. To solve the complexity of posteriors for dynamic processes, the posterior distributions with respect to state variables are constructed by a forward-backward recurrent neural network. One example is given to validate that the proposed method outperforms the comparative methods in modeling complex nonlinearities.

Keywords: Fault detection and diagnosis, Machine learning, Time series modelling
Abstract: The presence of downhole faults compromises the safety and also leads to increased maintenance costs in complex geological drilling processes. In order to achieve timely and accurate detection of downhole faults, a systematic fault detection method is proposed based on the Multivariate Generalized Gaussian Distribution (MGGD) and the Kullback Leibler Divergence (KLD). Uncorrelated components are obtained from the original drilling process signals using the principle component analysis; then, the distribution of components is estimated using the MGGD; afterwards, the KLD is calculated based on a deduced analytic formula; last, the downhole faut is detected by comparing the calculated KLD with the alarm threshold obtained from normal data. The effectiveness and practicality of the proposed method are demonstrated by application to a real drilling process.

Keywords: Machine learning, Fault detection and diagnosis
Abstract: In the Biotechnology 4.0 paradigm, process analytical technology (PAT) tools are being increasingly deployed in biomanufacturing to gain improved process insights through extensive use of advanced and automated sensing techniques. Critical parameters, such as pH, dissolved oxygen (DO), temperature and metabolite concentrations, are routinely measured and controlled in a cell culture process. While these extensive networks of sensors generate critical process information and insights, they are also prone to failures and malfunctions. In this paper, we propose a condition-based maintenance (CbM) framework for real-time sensor-health management, with a focus on fault detection, diagnosis, and prognostics. To this effect, a slow-feature analysis (SFA)-based platform is proposed for the detection and diagnosis of sensor- health. For health prognostics, a Gaussian process (GP) model is proposed for forecasting the remaining useful life (RUL) of the sensor along with the probability of failure. The efficacy of the proposed sensor-heath management strategy is demonstrated in a biomanufacturing process.

Keywords: Machine learning, Hybrid and switched systems modeling, Mechanical and aerospace estimation
Abstract: In performance tuning of many electromechanical devices, well-trained operators are in great demand. However, manual tuning is costly and time-consuming, and thus do not conform to the trend of smart manufacturing. Microwave filters are typical electromechanical devices. Their tuning performance is limited by low extraction accuracy and high dimensionality of circuit features. In this paper, a hybrid modeling method based on neural networks is proposed to get better tuning performance. First, a curve-shape-based modeling method using Convolutional Neural Networks is presented to bypass the cumbersome extraction of circuit features. Second, an multi-model optimized fusion model based on Elman Neural Networks is constructed to cope with the high-dimensional property of circuit features, and further improve modeling accuracy. The effectiveness of the hybrid modeling method is demonstrated through experiments. It achieves better tuning performance with fewer samples compared with two single modeling methods.

Keywords: Stochastic system identification, Randomized methods, Nonlinear system identification
Abstract: In classical paradigm of model identification, a single prediction value is returned as a point estimate of the output. Recently, the interval prediction model (IPM) has been receiving increasing attentions. Different from generic models, an IPM gives an interval of confidence as the prediction that covers the majority of training data while being as tight as possible. However, due to the randomness of sampling training data, the reliability of IPM constructed is uncertain. In this paper, we focus on a general class of IPMs where a fraction of data samples can be discarded to pursue robustness, and establish an appropriate a posteriori reliability guarantee. It relies on counting the "decisive" constraints associated with the optimal solution, and generally leads to reduced conservatism and better estimation performance than the existing performance bounds. Moreover, the guarantee holds irrespective of the data generation mechanism, which informs the decision maker of the prediction confidence in the absence of precise knowledge about data distribution. Its effectiveness is illustrated based on numerical examples.

Keywords: Fault detection and diagnosis, Time series modelling, Frequency domain identification
Abstract: Based on the reflectometry phenomenon and the behavior of an acoustic signal in a gas pipeline, this work proposes a fault location test for pipelines, which is formally justified for an infinite-dimension model of acoustic wave propagation in a closed conduit with viscous absorption. The test consists of disturbing the medium by an acoustic pulse at one extreme of the pipeline and of registering the transient response at an observation point. In this way, the waveform of the transient response of the pressure allows distinguishing the pattern of a healthy system from a pipeline with diverse faults and to allow locating the position of the damage.

Keywords: Filtering and smoothing, Machine learning, Bayesian methods
Abstract: The chemical process industry makes increasingly use of a diversity of data collectors, that should be properly integrated to build effective solutions for process monitoring, control and optimization. Concerning the assessment of products properties, one of the most common scenarios involve the collection of data from plant laboratories that provide more accurate measurements at lower rates, together with more frequent measurements or predictions of lower quality. Soft sensors and online analyzers are examples of viable alternatives for acquiring more frequent and updated information, although with a higher uncertainty. All of these data collectors have informative value and should be considered when it comes to estimate key product attributes. This is the goal of fusion methods, whose importance grows together with the increase in the number of sensors and data sources available. In this article, two fusion schemes that address prevailing characteristics of industrial data are proposed and compared: one version of the classic tracked Bayesian fusion scheme (TBF) and a novel modification of the track-to-track algorithm, designated as bias-corrected track-to-track fusion (BCTTF). The proposed methodologies are able to cope with the multirate nature of data and irregularly sampled measurements that present different uncertainty levels. An application to a real industrial case study shows that BCTTF presents better prediction performance, higher alarm identification sensitivity and leads to a smoother estimated signal.

Keywords: Fault detection and diagnosis, Machine learning, Time series modelling
Abstract: Canonical correlation analysis (CCA) is widely used as a supervised learning method to extract correlations between process and quality datasets. When used to extract relations between current data and historical data, CCA can also be regarded as an auto-regressive modeling method to capture dynamics. Various dynamic CCA algorithms were developed in the literature. However, these algorithms do not consider strong dependence existing in adjacent samples, which may lead to unnecessarily large time lags and inaccurate estimation of current values from historical data. In this paper, a dynamic weighted CCA (DWCCA) algorithm is proposed to address this issue with a series of polynomial basis functions. DWCCA extracts dynamic relations by maximizing correlations between current data and a weighted representation of past data, and the weights rely only on a limited number of polynomial functions, which removes the negative effect caused by strongly collinear neighboring samples. After all the dynamics are exploited, static principal component analysis is then employed to further explore the cross-correlations in the dataset. The Tennessee Eastman process is utilized to demonstrate the effectiveness of the proposed DWCCA method in terms of prediction efficiency and collinearity handling.

Keywords: Machine learning, Fault detection and diagnosis, Identifiability
Abstract: This work presents a novel approach to calculate classification observability using a supervised autoencoder (SAE) neural network (NN) for classification. This metric is based on a minimal distance between every two classes in the latent space defined by the hidden layers of the auto-encoder. Quantification of classification observability is required to address whether the available sensors in a process are sufficient to observe certain outputs (phenomenon) and which additional measurements are to be included in the dataset to improve classification accuracy. The efficacy of the proposed method is illustrated through case-studies for the Tennessee Eastman Benchmark Process.

Keywords: Machine learning, Learning for control, Adaptive gain scheduling autotuning control and switching control
Abstract: A database-driven PID (DD-PID) control method is one of the effective control methods for nonlinear systems. In the conventional DD-PID control method, there is a problem that the calculation cost and required memory for creating an optimal database are large. For the above problem, this paper proposes a method to implement the DD-PID controller with small-sized sub-databases. In the proposed method, one database that includes past I/O data and PID gains are created, and the database is updated in an offline manner. Moreover, sub-databases are constructed by clustering the created database using the k-means clustering method. The number of clusters for k-means clustering is determined automatically based on kernel functions. The effectiveness of the proposed method is presented by numerical examples.

Keywords: Machine learning, Consensus and Reinforcement learning control
Abstract: Over the last ten years, we have seen a significant increase in industrial data, tremendous improvement in computational power, and major theoretical advances in machine learning. This opens up an opportunity to use modern machine learning tools on large-scale nonlinear monitoring and control problems. This article provides a survey of recent results with applications in the process industry.

Keywords: Learning for control, Randomized methods, Model reference adaptive control
Abstract: Reinforcement Learning has been successfully applied to the problem of tuning PID controllers in several applications. The existing methods often utilize function approximation, such as neural networks, to update the controller parameters at each time-step of the underlying process. In this work, we present a simple finite-difference approach, based on random search, to tuning linear fixed-structure controllers. For clarity and simplicity, we focus on PID controllers. Our algorithm operates on the entire closed-loop step-response of the system and iteratively improves the PID gains towards a desired closed-loop response. This allows for prescribing stability requirements into the reward function without any modeling procedures.

Keywords: Learning for control, Consensus and Reinforcement learning control, Nonlinear adaptive control
Abstract: Deep reinforcement learning (DRL) has seen several successful applications to process control. Common methods rely on a deep neural network structure to model the controller or process. With increasingly complicated control structures, the closed-loop stability of such methods becomes less clear. In this work, we focus on the interpretability of DRL control methods. In particular, we view linear fixed-structure controllers as shallow neural networks embedded in the actor-critic framework. PID controllers guide our development due to their simplicity and acceptance in industrial practice. We then consider input saturation, leading to a simple nonlinear control structure. In order to effectively operate within the actuator limits we then incorporate a tuning parameter for anti-windup compensation. Finally, the simplicity of the controller allows for straightforward initialization. This makes our method inherently stabilizing, both during and after training, and amenable to known operational PID gains.

Keywords: Dynamic Networks
Abstract: Quantum variational algorithms have garnered significant interest recently, due to their feasibility of being implemented and tested on noisy intermediate scale quantum (NISQ) devices. We examine the robustness of the quantum approximate optimization algorithm (QAOA), which can be used to solve certain quantum control problems, state preparation problems, and combinatorial optimization problems. We demonstrate that the error of QAOA simulation can be significantly reduced by robust control optimization techniques, specifically, by sequential convex programming (SCP), to ensure error suppression in situations where the source of the error is known but not necessarily its magnitude. We show that robust optimization improves both the objective landscape of QAOA as well as overall circuit fidelity in the presence of coherent errors and errors in initial state preparation.

Keywords: Subspace methods
Abstract: Adiabatic elimination is a perturbative model reduction technique based on timescale separation and often used to simplify the description of composite quantum systems. We here analyze a quantum experiment where the perturbative expansion can be carried out to arbitrary order, such that: (i) we can formulate in the end an exact reduced model in quantum form; (ii) as the series provides accuracy for ever larger parameter values, we can discard any condition on the timescale separation, thereby analyzing the intermediate regime where the actual experiment is performing best; (iii) we can clarify the role of some gauge degrees of freedom in this model reduction technique.

Keywords: Continuous time system estimation, Identification for control, Dynamic Networks
Abstract: Additional noise in a quantum system can be detrimental to the performance of a quantum coherent feedback control system. This paper proposes a Linear Matrix Inequality (LMI) approach to construct an optimal quantum realization of a given Linear Time-Invariant (LTI) system. The quantum realization problem is useful in designing coherent quantum feedback controllers. An optimal method is proposed for solving this problem in terms of a finite horizon quadratic performance index, which is related to the amount of quantum noise appearing at the system's output. This cost function provides a measure of how much the additional quantum noise in the coherent controller will alter the feedback control system.

Keywords: Identifiability
Abstract: Quantum sensing, utilizing quantum techniques to extract key information of a quantum (or classical) system, is a fundamental area in quantum science and technology. For quantum sensors, a basic capability is to uniquely infer unknown parameters in a system based on measurement data from the sensors. In this paper, we investigate the capability of a class of quantum sensors for a spin-1/2 chain system with unknown parameters. The sensors are composed of qubits which are coupled to the object system and can be initialized and measured. We consider the capability of the single- and two-qubit sensors and show that the capability of single-qubit quantum sensors can be enhanced by adding an extra qubit into the sensor under a certain initialization and measurement setting.

Keywords: Fault detection and diagnosis
Abstract: The purpose of this paper is to design a coherent feedback controller for a Markovian jump linear quantum system suffering from a fault signal. The control objective is to bound the effect of the disturbance input on the output for the time-varying quantum system. We prove the relation between the H-infinity control problem, the dissipation properties, and the solutions of Riccati differential equations, by which the H-infinity controller of the Markovian jump linear quantum system is given by the solutions of Linear Matrix Inequalities (LMIs).

Keywords: Stochastic hybrid systems
Abstract: In this paper, we study the induced probabilistic Boolean dynamics for dynamical quantum networks subject to sequential quantum measurements. In this part of the paper, we focus on closed networks of quits whose states evolve according to a Schr"odinger equation. Sequential measurements may act on the entire network, or only on a subset of qubits. First of all, we show that this type of hybrid quantum dynamics induces probabilistic Boolean recursions as a Markov chain representing the measurement outcomes. Particularly, we establish an explicit and algebraic representation of the underlying recursive random mapping driving such induced Markov chains. Next, with local measurements, we establish a recursive way of computing such non-Markovian probability transitions.

Keywords: Stochastic hybrid systems
Abstract: In this paper, we study the induced probabilistic Boolean dynamics for dynamical quantum networks subject to sequential quantum measurements. In this part of the paper, we focus on closed networks of quits whose states evolutions are described by a continuous Lindblad master equation. When measurements are performed sequentially along such continuous dynamics, the quantum network states undergo random jumps and the corresponding measurement outcomes can be described by a probabilistic Boolean network. First of all, we show that the state transition of the induced Boolean networks can be explicitly represented through realification of the master equation. Next, when the open quantum dynamics is relaxing in the sense that it possesses a unique equilibrium as a global attractor, structural properties including absorbing states, reducibility, and periodicity for the induced Boolean network are direct consequences of the relaxing property. Finally, we show that for quantum consensus networks as a type of non-relaxing open quantum network dynamics, the communication classes of the measurement-induced Boolean networks are encoded in the quantum Laplacian of the underlying interaction graph.

Keywords: Estimation and filtering
Abstract: Theoretical developments in the field of quantum optics and quantum superconducting electrical circuits involving continuous measurement based feedback control as well as coherent control are an important prerequisites for advances in the domain of quantum technology. Within these perspectives, this paper considers positive real properties for a class of quantum systems whose quantum stochastic differential equation model involves annihilation operators only and then relates them to corresponding bounded real properties and consequently to physical realizability conditions developed earlier by the authors. Based on the positive real properties of these quantum systems, it is anticipated that it is possible to use the Brune algorithm in order to find an electrical circuit that can physically implement these quantum systems. This theory, in the case of one-port circuits, may be useful for the implementation of microwave circuits related to quantum filters found in the field of quantum computing.

Keywords: Estimation and filtering;Quantized systems
Abstract: This paper provides a procedure for building a one port impedance quantization involving annihilation operators only for a class of linear quantum systems having a positive real impedance transfer function matrix. Based on the positive real properties of these quantum systems, it is shown that it is possible to use the Brune algorithm in order to find an electrical circuit that can physically implement these quantum systems. This theory, illustrated for one port circuits may be useful for the implementation of superconducting microwave circuits used in quantum filters found in the field of quantum computing.

Keywords: Stochastic control and game theory, Synthesis of stochastic systems
Abstract: This paper is concerned with quadratic-exponential functionals (QEFs) as risk-sensitive performance criteria for linear quantum stochastic systems driven by multichannel bosonic fields. Such costs impose an exponential penalty on quadratic functions of the quantum system variables over a bounded time interval, and their minimization secures a number of robustness properties for the system. We use an integral operator representation of the QEF, obtained recently, in order to compute its infinite-horizon asymptotic growth rate in the invariant Gaussian state when the stable system is driven by vacuum input fields. The resulting frequency-domain formula expresses the QEF growth rate in terms of two spectral functions associated with the real and imaginary parts of the quantum covariance kernel of the system variables. We also discuss the computation of the QEF growth rate using homotopy and contour integration techniques and provide an illustrative numerical example with a two-mode open quantum harmonic oscillator.

Keywords: Stochastic control and game theory
Abstract: The control of flying qubits is crucial for the nterconnection of quantum information processing units in the future applications. Physically, this class of problems can be modeled by the radiation of opticalelds from a standing qubit (natural or artificial atoms). The photon statistics of the output field emitted from a quantum system coupled to multiple waveguides is complicated when the exciton number is not conserved, especially in presence of coherent driving that is crucial for control and optimization. In this paper, we use quantum stochastic differential equation (QSDE) todescribe the photon generation process, and derive the dynamical jumps induced by photon emission. Numerical simulations show that this model can be applied to analyze the manipulation process of single qubits.

Keywords: Synthesis of stochastic systems, Stochastic control and game theory
Abstract: This paper is concerned with a risk-sensitive optimal control problem for a feedback connection of a quantum plant with a measurement-based classical controller. The plant is a multimode open quantum harmonic oscillator driven by a multichannel quantum Wiener process, and the controller is a linear time invariant system governed by a stochastic differential equation. The control objective is to stabilize the closed-loop system and minimize the infinite-horizon asymptotic growth rate of a quadratic-exponential functional (QEF) which penalizes the plant variables and the controller output. We combine a frequency-domain representation of the QEF growth rate, obtained recently, with variational techniques and establish first-order necessary conditions of optimality for the state-space matrices of the controller.

Keywords: Nonlinear system identification
Abstract: Balancing the model complexity and the representation capability towards the process to be captured remains one of the main challenges in nonlinear system identification. One possibility to reduce model complexity is to impose structure on the model representation. To this end, this work considers the linear fractional representation framework. In a linear fractional representation the linear dynamics and the system nonlinearities are modeled by two separate blocks that are interconnected with one another. This results in a structured, yet flexible model structure. Estimating such a model directly from input-output data is not a trivial task as the involved optimization is nonlinear in nature. This paper proposes an initialization scheme for the model parameters based on the best linear approximation of the system and shows that this approach results in high quality models on a set of benchmark data sets.

Keywords: Nonparametric methods, Nonlinear system identification, Time series modelling
Abstract: Volterra series is especially useful for nonlinear system identification, also thanks to is capability to approximate a broad range of input-output maps. However, its identification from a finite set of data is hard, due to the curse of dimensionality. Recent approaches have shown how regularization strategies can be useful for this task. In this paper, we propose a new regularization network for Volterra models identification. It relies on a new kernel given by the product of basic building blocks. Each block contains some unknown parameters that can be estimated from data using marginal likelihood optimization or cross-validation. In comparison with other algorithms proposed in the literature, numerical experiments show that our approach allows to better select the monomials that really influence the system output, much increasing the prediction capability of the model. The method immediately extends also to polynomial NARMAX models.

Keywords: Nonlinear system identification, Identification for control, Frequency domain identification
Abstract: Cortical responses to external mechanical stimuli recorded by electroencephalography have demonstrated complex nonlinearity with fast dynamics. Hence, the modelling of the human nervous system plays a crucial role in studying the function of the sensorimotor system and can help in disentangling the sensory-motor abnormalities in functional movement disorders. In this paper, a non-parametric model is proposed based on locally-linear neuro-fuzzy structures trained by an evolutive algorithm named local linear model tree. In particular, a simulation model as well as a multi-step predictor model is considered to describe the nonlinear dynamics governing the cortical response. The proposed modelling method is applied to an experimental dataset, where brain activities from ten young healthy subjects are recorded by electroencephalography signals while robotic manipulations were applied to their wrist joint. The obtained results are satisfactory and are also compared to those achieved with different modelling strategies applied to the same benchmark.

Keywords: Nonlinear system identification
Abstract: The Nonlinear Auto-regressive eXogenous input (NARX) model has been widely used in nonlinear system identification. It's chief disadvantages are that it is a black-box model that suffers from the curse of dimensionality, in that the number of parameters increases rapidly with the nonlinearity degree. One approach to dealing with these problems involves decoupling the nonlinearity, but this requires solving a non-convex optimization problem. Solving non-convex optimization problems has always been challenging due to the possibility of getting trapped in a sub-optimal local optima. As a result, these kinds of optimization problems are sensitive to the initial solution. Providing an appropriate initial solution can increase the likelihood of finding the globally optimal solution. In this paper, an initialization technique that uses the polynomial coefficients in a full, albeit low order, NARX model is proposed. This technique generates a tensor from the coefficients in the from full polynomial NARX model and applies a tensor factorization in order to generate an appropriate starting point for decoupled polynomial NARX model optimization problem. The proposed technique is applied to nonlinear benchmark problem and the results are promising.

Keywords: Nonlinear system identification
Abstract: A persisting challenge in nonlinear dynamical modelling is parameter inference from data. Provided that an appropriate model structure was selected, the identification problem is profoundly affected by a choice of initialisation. A particular challenge that may arise is initialisation within a region of the parameter space where the model is not contractive. Exploring such regions is not feasible using the conventional optimisation tools for they require a bounded evaluation of the cost. This work proposes an unconstrained multiple shooting technique, able to mitigate stability issues during the optimisation of nonlinear state-space models. The technique is illustrated on simulation results of a Van der Pol oscillator and benchmark results on a Bouc-Wen hysteretic system.

Keywords: Experiment design
Abstract: Assessment criteria for design of wind turbines controller are discussed since conventional control performance criteria are not sufficient to evaluate the mechanical loads as dependency of the controller type and settings. This will be presented and discussed using the example of the active power control of wind turbines. In contrast to the nominal operation of wind turbines divided into power optimization in the partial and power limitation in the full load region, the power output is guided by an external power reference signal. The reference signal may be delivered either directly by higher-level load frequency controller of the power system or by the wind farm controller. In both cases the external variation of the power to be delivered has an enormous influence on the dynamics and mechanical loads of the wind turbine. To quantify these loads that occur during power tracking operation the Damage Equivalent Load amplitude as appropriated load assessment criteria is described and prepared for control design.

Keywords: Frequency domain identification
Abstract: The control system of the superconducting electron linear accelerator ELBE is planned to be upgraded by a beam-based feedback. As the design of the feedback algorithm enters its preliminary stage, the problem of analyzing the contribution of various disturbances to the development of the electron beam instabilities becomes highly relevant. In this paper we exploit the radio frequency (RF) phase and amplitude noise data measured at ELBE to create a behavioral model in Simulink. By modeling the interaction between a RF electromagnetic field and an electron bunch traversing a bunch compressor we analyze how the addition of RF noise impacts the electron beam properties, such as energy, duration and arrival time.

Keywords: Mechanical and aerospace estimation, Errors in variables identification
Abstract: Electrical Impedance Tomography (EIT) can be used to study the hydrodynamic characteristics in multiphase flows such as gas holdup in bubble columns, air core in hydrocyclone etc. In EIT, the main objective is to estimate the electrical properties (conductivity distribution) of an object in a region of interest based on the surface voltage measurements. The main challenge in such reconstruction (estimation of conductivity distribution) is the low spatial resolution. In this paper, a sparse optimization approach for image reconstruction in EIT is presented. The main idea presented in this article is based on considering the L1 norm on the data term which enhances reconstruction of conductivity distributions with sharp changes near phase boundaries. Further, this method is also robust to outliers in the data. The accuracy of the proposed method is demonstrated with the help of two phantoms and a comparison with the existing methods is also presented.

Keywords: Time series modelling
Abstract: Superconducting accelerating cavities for continuous wave low-current particle accelerators requires a tight resonance control to optimize the RF power costs and to minimize the beam delivery downtime. When the detuning produced by radiation pressure becomes comparable to the RF bandwidth, the monotonic instability starts to affect the cavity operation. When this instability is triggered by external vibrations or drifts, the accelerating field amplitude drops rapidly, and the beam acceleration has to be stopped. Past experiments showed that using an integral control of the piezoelectric tuners installed on the cavity prevents the adverse effects of the monotonic instability. This paper derives theoretically why an integral controller is an effective way to counteract the monotonic instability. To perform the study a linearized state-space model of the cavity is derived. Simulations and experiments in a superconducting test facility indicate that the use of this kind of control has the additional benefit of bringing the cavities to the resonance condition automatically.

Keywords: Bayesian methods, Filtering and smoothing
Abstract: A novel robust Kalman filter based on Gaussian-Student's t mixture (GSTM) distribution is proposed to address the filtering problem of a linear system with non-stationary heavy-tailed measurement noise. The mixing probability is recursively estimated by using its previous estimates as prior information, and the state vector, the auxiliary parameter, the Bernoulli random variable and the mixing probability are jointly estimated utilizing the variational Bayesian method. The excellent performance of the proposed robust Kalman filter, compared with the existing state-of-the-art filters, is illustrated by a target tracking simulation results under the case of non-stationary heavy-tailed measurement noise.

Keywords: Bayesian methods, Frequency domain identification, Input and excitation design
Abstract: Recently, the research of identification input design for Bayesian methods has been actively investigated. Either the problem is formulated as a non-convex problem with difficulty in solving or relaxed as a convex problem with a price of some conservativeness. In this contribution, a new minimum power input design problem is formulated by viewing the input as a stochastic process. We seek the minimum energy input with variance constraints over a frequency band. By exploiting the generalized Kalman-Yakubovich-Popov lemma, the stochastic consideration facilitates the input design problem to be presented as a convex problem whose decision variables are a finite number of autocorrelation coefficients. We obtain the autocorrelation coefficients of the desired stochastic input signal by solving the convex problem and extend them by the maximum entropy extension. Then, a specific identification input is sampled from the obtained stochastic process. Simulations results demonstrate the effectiveness of the proposed method.

Keywords: Bayesian methods, Learning for control, Fault detection and diagnosis
Abstract: Cascaded controller tuning is a multi-step iterative procedure that needs to be performed routinely upon maintenance and modification of mechanical systems. An automated data-driven method for cascaded controller tuning based on Bayesian optimization is proposed. The method is tested on a linear axis drive, modeled using a combination of first principles model and system identification. A custom cost function based on performance indicators derived from system data at different candidate configurations of controller parameters is modeled by a Gaussian process. It is further optimized by minimization of an acquisition function which serves as a sampling criterion to determine the subsequent candidate configuration for experimental trial and improvement of the cost model iteratively, until a minimum according to a termination criterion is found. This results in a data-efficient procedure that can be easily adapted to varying loads or mechanical modifications of the system. The method is further compared to several classical methods for auto-tuning, and demonstrates higher performance according to the defined data-driven performance indicators. The influence of the training data on a cost prior on the number of iterations required to reach optimum is studied, demonstrating the efficiency of the Bayesian optimization tuning method.

Keywords: Bayesian methods, Learning for control, Nonlinear system identification
Abstract: Tensioned cable nets can be used as supporting structures for the efficient construction of lightweight building elements, such as thin concrete shell structures. To guarantee important mechanical properties of the latter, the tolerances on deviations of the tensioned cable net geometry from the desired target form are very tight. Therefore, the form needs to be readjusted on the construction site. In order to employ model-based optimization techniques, the precise identification of important uncertain model parameters of the cable net system is required. This paper proposes the use of Gaussian process regression to learn the function that maps the cable net geometry to the uncertain parameters. In contrast to previously proposed methods, this approach requires only a single form measurement for the identification of the cable net model parameters. This is beneficial since measurements of the cable net form on the construction site are very expensive. For the training of the Gaussian processes, simulated data is efficiently computed via convex programming. The effectiveness of the proposed method and the impact of the precise identification of the parameters on the form of the cable net are demonstrated in numerical experiments on a quarter-scale prototype of a roof structure.

Keywords: Bayesian methods, Machine learning
Abstract: For robust Gaussian process regression problems where the measurements are contaminated by outliers, a likelihood/measurement noise model with heavy-tailed distributions should be used to improve the prediction performance. In this paper, we propose to use a G-confluent distribution as the measurement noise model and a coordinate ascent variational inference method to infer the overall statistical model. In contrast with the commonly used Student's t distribution, the G-confluent distribution can also be written as a Gaussian scale mixture, but its inverse scale follows a Beta distribution rather than a Gamma distribution, and its main advantage is that it is more flexible for modeling outliers while being equally suitable for variational inference. Numerical simulations based on benchmark data show that the G-confluent distribution performs better than or as well as the Student's t distribution.

Keywords: Bayesian methods, Nonlinear system identification, Nonparametric methods
Abstract: We propose a framework for modeling structured nonlinear systems using nonparametric Gaussian processes. In particular, we introduce a two-layer stochastic model of latent interconnected Gaussian processes suitable for modeling Hammerstein-Wiener and Wiener-Hammerstein cascades. The posterior distribution of the latent processes is intractable because of the nonlinear interactions in the model; hence, we propose a Markov Chain Monte Carlo method consisting of a Gibbs sampler where each step is implemented using elliptical-slice sampling. We present the results on two example nonlinear systems showing that they can effectively be modeled and identified using the proposed nonparametric modeling approach.

Keywords: Bayesian methods, Nonparametric methods, Machine learning
Abstract: In this paper, the hierarchical Bayesian method for regularized system identification is introduced. To this end, a hyperprior distribution is considered for the regularization matrix and then, the impulse response and the regularization matrix are jointly estimated based on a maximum a posteriori (MAP) approach. Toward introducing a suitable hyperprior, we decompose the regularization matrix using Cholesky decomposition and reduce the estimation problem to the cone of upper triangular matrices with positive diagonal entries. Following this, the hyperprior is introduced on a designed sub-cone of this set. The method differs from the current trend in regularized system identification from various aspect, e.g., the estimation is performed by solving a single stage problem. The MAP estimation problem reduces to a multi-convex optimization problem and a sequential convex programming algorithm is introduced for solving this problem. Consequently, the proposed method is a computationally efficient strategy specially when the regularization matrix has a large size. The method is numerically verified on benchmark examples. Owing to the employed full Bayesian approach, the estimation method shows a satisfactory bias-variance trade-off.

Keywords: Bayesian methods, Nonparametric methods, Machine learning
Abstract: This paper presents a novel kernel-based system identification method, which promotes low complexity of the model in terms of the McMillan degree of the system. The regularization matrix is characterized as a linear combination of pre-selected rank-one matrices with unknown hyperparameter coefficients, and the hyperparameters are derived using a maximum a posteriori estimation approach. Each basis matrix is the optimal regularization matrix for a first-order system. With this basis matrix selection, the McMillan degree of the identified model is upper-bounded by the rank of the regularization matrix, which in turn is equal to the cardinality of the hyperparameters. For this reason, a sparsity-promoting prior is chosen for hyperparameter tuning. The resulting optimization problem has a difference of convex program form which can be efficiently solved. The advantages of the proposed method are that the identified model has a low-complexity structure and that an improved bias-variance trade-off is achieved. Numerical results confirm that the proposed method achieves a better bias-variance trade-off as well as a better fit to the model compared to both the empirical Bayes method and the atomic-norm regularization.

Keywords: Bayesian methods, Particle filtering/Monte Carlo methods, Filtering and smoothing
Abstract: A suboptimal two-stage algorithm has been proposed to solve nonlinear estimation problems consist in comparison of measured and reference samples. The new algorithm consists of preliminary processing of measurements, subsampling and simplification of the errors model in nonlinear algorithm. A significant increase in computational performance determines the novelty of the presented algorithm. The effective application of the two-stage suboptimal algorithm is illustrated by an example of gravity-aided navigation.

Keywords: Fault detection and diagnosis, Bayesian methods
Abstract: Following the intuition that not all latent variables in probabilistic principal component analysis method shifts simultaneously, this paper proposes a spike-and-slab regularization technique for nonlinear fault detection and isolation. Different from the existing probabilistic latent variable models, a spike-and-slab prior is introduced to downweight the irrelevant information of latent variables for the discriminative model. The resulting latent subspace supported by regularization parameters is not only sensitive to the informative variables, but it also eliminates the influence of the non-informative ones. The feasibility and efficiency of the proposed approach will be tested on an industrial methanol distillation dataset. Moreover, the performance will be compared with conventional probabilistic latent variables methods.

Keywords: Nonparametric methods, Bayesian methods, Identification for control
Abstract: We present a method for data-based estimation of the H2-norm of a linear time-invariant system from input-output data in a probabilistic setting by employing the recent advances in Gaussian process system identification using stable-spline kernels. Advantages of this starting point include that the norm can be estimated for the continuous-time system and over infinite horizon, even though only a finite number of measurements are available. We approximate the H2-norm distribution as Gaussian, whose expectation can even be obtained analytically, while we use a numerical scheme based on Gaussian process quadrature for the variance. Not only do we utilize the posterior variance of the Gaussian process to derive an error estimate for the H2-norm, but also to tune the estimation by optimizing the input sequence. The performance of the developed scheme is thoroughly evaluated in simulation.

Keywords: Identification for control, Nonlinear system identification, Bayesian methods
Abstract: In a polymer production process, a special reactor is used to adjust the viscosity, i.e., chain length of the polymer. This reactor has several control variables mainly in manually control. For future automatic control concepts, such a reactor is modeled from data with a linear (regularized FIR) and a nonlinear state space model (LMSSN). A model predictive control approach is presented in simulation.

Keywords: Learning for control, Bayesian methods, Stochastic system identification
Abstract: For linear control systems, the so-called controllability Gramian has played an important role to quantify how effectively the dynamical states can be driven to a target one by a suitable driving input. On the other hand, thanks to the availability of Big Data, the Gaussian process state space model, a data-driven probabilistic modeling framework, has attracted much attention in recent years. In this paper, we newly introduce the concept of the controllability Gramian for nonlinear dynamics represented by the Gaussian process state space model, aiming at better understanding of this new modeling framework. Then, its effective calculation method and application to model sparsification are investigated.

Keywords: Learning for control, Nonlinear system identification, Bayesian methods
Abstract: Enabling analysis of non-linear systems in linear form, the Koopman operator has been shown to be a powerful tool for system identification and controller design. However, current data-driven methods cannot provide quantification of model uncertainty given the learnt model. This work proposes a probabilistic Koopman operator model based on Gaussian processes which extends the author’s previous results and gives a quantification of model uncertainty. The proposed probabilistic model enables efficient propagation of uncertainty in feature space which allows efficient stochastic/robust controller design. The proposed probabilistic model is tested by learning stable nonlinear dynamics generating hand-written characters and by robust controller design of a bilinear DC motor.

Keywords: LPV system identification, Particle filtering/Monte Carlo methods, Bayesian methods
Abstract: Temperature estimation through infrared thermography is facing the lack of knowledge of the observed material's emissivity. The derivation of the physical equations lead to an ill-posed problem. A new Kriged Interacting Particle Kalman Filter is proposed. A state space model relates the measurements to the temperature and the Kalman filter equations yield a filter tracking the temperature over time. Moreover, a particle filter associated to Kriging prediction is interacting with a bank of Kalman filters to estimate the time-varying parameters of the system. The efficiency of the algorithm is tested on a simulated sequence of infrared thermal images.

Keywords: Nonparametric methods, Bayesian methods
Abstract: A long-standing problem for kernel-based regularization methods is their high computational complexity O(N^3), where N is the number of data points. In this paper, we show that for semiseparable kernels and some typical input signals, their computational complexity can be lowered to O(Nq2), where q is the output kernel’s semiseparability rank that only depends on the chosen kernel and the input signal.

Keywords: Closed loop identification, Estimation and filtering
Abstract: It is necessary to perform the system identification under severe numerical conditions in many practical applications. When less external test signals are available for parameter estimation from experimental data, the identification performance often suffers from numerical problems in the optimization procedure due to the less independent informative components, the influence of complicated noise, or the local minima problem. In this paper, a multi-point search based identification algorithm is investigated for system identification under severe numerical conditions. It introduces the output over-sampling scheme to collect the experimental input-output data, and extracts the information in time and space domains to complement information criterion for numerical optimization. Furthermore, the multi-point search is utilized to decrease the influence of local minima. The numerical simulation examples illustrate that the identification performance has been improved in the proposed algorithm.

Keywords: Experiment design, Machine learning, Estimation and filtering
Abstract: In this paper, we present a novel low-cost technique to estimate both the position and the speed of a permanent magnet synchronous motor (PMSM) by sensing its stray magnetic field. At an optimal radial and axial distance, a low-cost magnetoresistive sensor is placed outside at the back of the PMSM. The magnetic field values are recorded for one complete rotor revolution at a resolution of less than a degree for different speeds of operation. Gaussian Processes (GPs) are employed to find a mapping function between the magnetic field values of the permanent magnet and the absolute angular positions. Then, by using the learned GP as a measurement function with an Extended Kalman Filter (EKF), both the angular position and speed of a PMSM can be estimated efficiently. Furthermore, we observe that the magnetic field depends not only on the position but also on the angular speed. To address this, we extend the GP to incorporate multivariate inputs. In order to take the periodicity of the data into account, we employ a periodic kernel for the GP. Additionally, a linear basis function model (LBFM) is introduced to incorporate more training points while maintaining the same computational cost. The GP and LBFM approaches are evaluated with data from a real PMSM experiment setup, and the accuracy of the position and speed state estimation is verified against a high-resolution optical encoder used as ground truth.

Keywords: Filtering and smoothing, Estimation and filtering, Bayesian methods
Abstract: This paper continues the research devoted to the design of numerically stable square-root implementations for the maximum correntropy criterion Kalman filtering (MCC-KF). In contrast to the previously obtained results, here we reveal the first robust (with respect to round-off errors) method within the Cholesky factorization-based approach. The method is formulated in terms of square-root factors of the covariance matrices, i.e. it belongs to the covariance-type filtering methodology. Additionally, a numerically stable orthogonal transformation is utilized at each iterate of the algorithm for accurate propagation of the Cholesky factors involved. The results of numerical experiments illustrate a superior performance of the novel MCC-KF implementation compared to both the conventional algorithm and its previously published Cholesky-based variant.

Keywords: Filtering and smoothing, Estimation and filtering, Errors in variables identification
Abstract: The authors discuss the problem of how to monitor the coal/water pulsating bed in a jig with the use of a radiation density meter. The dynamic measurement error of changes in density depends on the time of measurement; its optimal value can be found for a given shape of density changes. An alternative method of the signal filtration is proposed using variable time of measurement during a cycle of pulsations as a function of the time derivative of the density changes. The shape of the density changes during one cycle varies slowly from a cycle to a cycle. This is why the time derivative of the density determined during one cycle can be used in the subsequent cycle to adapt periodically the algorithm generating the variable times of measurement during each cycle. The above time derivative can be calculated from the polynomial fit of stochastic data measured during the previous cycle. In this case, the dynamic error of the measurement MSE can be reduced significantly compared to the optimal constant time of the measurement. This methodology of signal filtration was applied in the simulation model and the results of simulation were compared with field measurements taken with the use of a conventional radiometric density meter.

Keywords: Filtering and smoothing, Estimation and filtering, Synthesis of stochastic systems
Abstract: Linear, discrete-time systems with state-multiplicative noise and delayed states are considered. The problem of robust Hoo general-type filtering is solved for these systems when the uncertainty in their deterministic parameters is of the polytopic-type. The obtained vertex-dependant solution is based on a modified Finsler lemma which leads to a simple set of LMIs condition. The included numerical example demonstrates the tractability and solvability of the proposed method.

Keywords: Filtering and smoothing, Fault detection and diagnosis
Abstract: Alarm filtering is a structurally simple, easy to implement, and effective method to improve industrial alarm systems. Owing to these advantages, alarm filters are widely used in industrial applications. Linear and quadratic are the main types of alarm filters. Although a linear filter can detect mean changes, it can not be used to detect variation changes. However, a quadratic filter can be used to detect both types of changes. Although this remarkable feature of quadratic filters has been addressed in the literature, no explicit performance analysis is performed yet. So, deriving an analytical solution for quadratic filters is of paramount importance. To this aim, we propose an analytical method for performance assessment and design of quadratic filters. On the other side, in industrial applications, many process variables are acquired. So one challenge is to identify the process variable that provides the best alarm performance after filtering. We will derive an analytical solution to this problem. Furthermore, we will prove that this optimal solution is a function of the statistical feature of historical data and alarm filter structure.

Keywords: Filtering and smoothing, Nonlinear system identification, Software for system identification
Abstract: Efficiency of using global navigation satellite system (GNSS) measurements for determining gravity anomalies (GA) at sea by solving filtering and smoothing problems based on GNSS and gravimeter data is studied. The GA, ship heaving, errors of GNSS and gravimeter measurements are presented as stochastic processes. The analysis is based on the standard deviations of the GA estimation errors, calculated at different heaving parameters and in different modes of GNSS data processing.

Keywords: Time series modelling
Abstract: This paper investigates the assessment of Granger causality (GC) between jointly Gaussian signals based on noisy or filtered measurements. To do so, a recent rank condition for inferring GC between jointly Gaussian stochastic processes is exploited. Sufficient conditions are derived under which GC can be reliably inferred from the second order moments of the noisy or filtered measurements. This approach does not require a model of the underlying Gaussian system to be identified. The noise signals are not required to be Gaussian or independent, and the filters may be noncausal or nonminimum-phase, as long as they are stable.

Keywords: Filtering and smoothing, Quantized systems, Networked embedded control systems
Abstract: In this paper, we propose sparse representation of FIR (Finite Impulse Response) feedback filters in delta-sigma modulators. The filter has a sparse structure, that is, only a few coefficients are non-zero, that stabilizes the feedback modulator, and minimizes the maximum magnitude of the noise transfer function at low frequencies. The optimization is described as an L1 minimization with linear matrix inequalities (LMIs), based on the generalized KYP (Kalman-Yakubovich-Popov) lemma. A design example is shown to illustrate the effectiveness of the proposed method.

Keywords: Machine learning
Abstract: The nearest-centroid classifier is a simple linear-time classifier based on computing the centroids of the data classes in the training phase, and then assigning a new datum to the class corresponding to its nearest centroid. Thanks to its very low computational cost, the nearest-centroid classifier is still widely used in machine learning, despite the development of many other more sophisticated classification methods. In this paper, we propose two sparse variants of the nearest-centroid classifier, based respectively on ℓ₁ and ℓ₂ distance criteria. The proposed sparse classifiers perform simultaneous classification and feature selection, by detecting the features that are most relevant for the classification purpose. We show that training of the proposed sparse models, with both distance criteria, can be performed exactly (i.e., the globally optimal set of features is selected) and at a quasi-linear computational cost. The experimental results show that the proposed methods are competitive in accuracy with state-of-the-art feature selection techniques, while having a significantly lower computational cost.

Keywords: Time series modelling, Machine learning, Quantized systems
Abstract: Clustering is an unsupervised learning technique that is useful when working with a large volume of unlabeled data. Complex dynamical systems in real life often entail data streaming from a large number of sources. Although it is desirable to use all source variables to form accurate state estimates, it is often impractical due to large computational power requirements, and sufficiently robust algorithms to handle these cases are not common. We propose a hierarchical time series clustering technique based on symbolic dynamic filtering and Granger causality, which serves as a dimensionality reduction and noise-rejection tool. Our process forms a hierarchy of variables in the multivariate time series with clustering of relevant variables at each level, thus separating out noise and less relevant variables. A new distance metric based on Granger causality is proposed and used for the time series clustering, as well as validated on empirical data sets. Experimental results from occupancy detection and building temperature estimation tasks show fidelity to the empirical data sets while maintaining state-prediction accuracy with substantially reduced data dimensionality.

Keywords: Continuous time system estimation
Abstract: This paper presents an algorithm for estimating the parameters of a biased sinusoidal signal. The proposed method uses the output signals of a second order generalized integrator without adaptation on its resonant frequency to derive a linear regression equation where the unknown parameters are a nonlinear combination of bias and frequency of the input signal. The global stability of the method is proven. Remarkably, the proposed method represents the minimum-order estimator known for the problem under consideration, being implementable by a 4th-order adaptive system. Simulation results and comparisons with existing methods show the accurate estimation capability of the proposed approach.

Keywords: Continuous time system estimation
Abstract: In this paper we address the problem of identifying a continuous-time deterministic system utilising sampled-data with instantaneous sampling. We develop an identification algorithm based on Maximum Likelihood. The exact discrete-time model is obtained for two cases: i) known continuous-time model structure and ii) using Kautz basis functions to approximate the continuous-time transfer function. The contribution of this paper is threefold: i) we show that, in general, the discretisation of continuous-time deterministic systems leads to several local optima in the likelihood function, phenomenon termed as aliasing, ii) we discretise Kautz basis functions and obtain a recursive algorithm for constructing their equivalent discrete-time transfer functions, and iii) we show that the utilisation of Kautz basis functions to approximate the true continuous-time deterministic system results in convex log-likelihood functions. We illustrate the benefits of our proposal via numerical examples.

Keywords: Continuous time system estimation
Abstract: A novel adaptive identifier is developed for nonlinear time-delay systems composed of linear, Lipschitz and non-Lipschitz components. To begin with, an identifier is designed for uncertain systems with a priori known delay values, and then it is generalized for systems with unknown delay values. The algorithm ensures the asymptotic parameter estimation and state observation by using gradient algorithms. The unknown delays and plant parameters are estimated by using a special equivalent extension of the plant equation. The algorithms stability is presented by solvability of linear matrix inequalities.

Keywords: Continuous time system estimation
Abstract: In this paper we apply a continuous-time system identification method, known as the Simplified Refined Instrumental Variable method for Continuous-time systems (SRIVC), to the problem of estimating membrane properties of vestibular Type II hair cells. Due to the non-ideal characteristics of the experimental system, additional parameters, other than those of the membrane are required to be estimated. The SRIVC algorithm is modified to allow known poles and zeros to be forced into the estimator. This modified algorithm is then applied to the identification of the membrane properties of vestibular Type II hair cells, yielding results commensurate with typically accepted values.

Keywords: Continuous time system estimation, Bounded error identification, Identification for control
Abstract: For feedback control designs, one of the fundamental problems is to handle the unknown system dynamics. In this paper, an alternative unknown system dynamics estimator (USDE) with low-pass filter operations is presented based on an invariant manifold method, in which we only need to set a scalar, the filter parameter. The convergence performance and robustness of this USDE are analysed in both the time-domain and frequency-domain. To circumvent the sensitiveness to the measurement noise, a further enhanced USDE (EUSDE) with two-layer of low-pass filters is constructed. With the proposed estimators, all time-varying components, such as unmodeled dynamics, nonlinearities and external disturbances, can be viewed as a lumped unknown system dynamics term and then effectively estimated even in the presence to fair measurement noise. The function of these estimators is the same as the well-known disturbance observer (DOB) and extended state observer (ESO). Hence, they can be easily incorporated into control schemes. Numerical simulation results are presented to show the effectiveness of the proposed estimation schemes.

Keywords: Continuous time system estimation, Estimation and filtering
Abstract: The aim of this work is to propose a design methodology of observers for a class of Lipschitz nonlinear dynamical systems with sampled measurements by using the differential mean value theorem (DMVT) which allows us to transform the nonlinear part of the estimation error dynamics into a linear parameter varying (LPV) system. The designed observer must ensure the stability of the estimation error subject to a sampled measurements. An LMI-based minimization problem is provided to ensure the stability and the existence of the observer using Lyapunov theory. Thus, the measurements sampling period is included in the LMI as a decision parameter. Indeed, this allows to widen the sampling period as much as possible, which helps optimization of energy consumption while guaranteeing the convergence of the observer. Finally, to illustrate the performance of the proposed methodology, a numerical example is presented.

Keywords: Continuous time system estimation, Estimation and filtering, Stochastic system identification
Abstract: Recently, a new indirect approach method for continuous-time system identification has been proposed that provides complete freedom on the number of poles and zeros of the linear and time-invariant continuous-time model structure. However, this procedure has reliability issues, as it may deliver unstable estimates even if the initialisation model and true system are stable. In this paper, we propose a method to overcome this problem. By generating ellipsoids that contain parameter vectors whose coefficients yield stable polynomials, we introduce a convex constraint in the indirect prediction error method formulation, and show that the proposed method enjoys optimal asymptotic properties while being robust in small and noisy data set scenarios. The effectiveness of the novel method is tested through extensive simulations.

Keywords: Continuous time system estimation, Filtering and smoothing
Abstract: The use of algebraic differentiators in the context of asymptotic continuous-time parameter estimation is discussed. The estimation problem is analyzed within a least squares optimization context. Bounds for the error stemming from high frequency disturbances and the approximation of the derivatives are derived. It is shown that with higher frequencies the error stemming from the disturbances decreases and that the filter parameters can be used to adjust the convergence of this error to zero. An observer with assignable error dynamics for the online estimation is also proposed. A simulation is carried out to evaluate the results and compare the proposed observer with the recursive solution of the least squares problem.

Keywords: Continuous time system estimation, Mechanical and aerospace estimation
Abstract: This work is motivated by a case study of a mechanical system where a sensor bias yields loose of observability for certain values of time-varying parameters. Two solutions are proposed: a nonlinear gradient-based observer that requires the persistency of excitation of the system trajectories and a switched observer that imposes an average dwell-time requirement. For both observers, asymptotic convergence of the estimates is proven. The theoretical results are supported by illustrative numerical simulations.

Keywords: Continuous time system estimation, Nonlinear system identification
Abstract: This paper is devoted to a frequency estimation of a pure sinusoidal signal in finite-time. The parameterization is based on applying delay operators to a measurable signal. The result is the first-order linear regression model with one parameter, which depends on the signal frequency. The proposed method of finite-time estimation consists of two steps. On the first step, the standard gradient descent method is used to estimate the regression model parameter. On the next step using algebraic equations, finite-time frequency estimate is found. The described method does not require measuring or calculating derivatives of the input signal and uses one integrator for the gradient method and another one for the finite-time estimation. The efficiency of the proposed approach is demonstrated through the set of numerical simulations.

Keywords: Continuous time system estimation, Recursive identification, Identification for control
Abstract: This paper proposes a novel method for the simultaneous estimation of the coefficients and the delay term of a delayed fractional order system. Because of the practicality aspect of the non-ideal step inputs, such inputs are used in this paper for the first time to identify a fractional order system. To this end, the proposed identification procedure is separately described for two types of fractional order systems, i.e., including both non-delayed and delayed systems. For the non-delayed system, a fractional order integral approach is developed, and for the delayed system, a filtering approach is investigated to make the delay term to be explicitly appeared in the parameters vector. In simulation results, some illustrative examples, covering both non-delayed and delayed systems, are given to demonstrate the validity of the proposed method.

Keywords: Experiment design, Grey box modelling, Continuous time system estimation
Abstract: In this paper, a data driven approach is used to obtain the static gain of dc--dc power converters in terms of the duty cycle and a set of linear coefficients. A known number of measurements, dependent on the dc--dc converter topology, are used to built-in a rational function obtained by linear coefficients. This solution shows how to use measurements to determine a function to represent the static gain of dc--dc power converters in the continuous-conduction mode (CCM). To validate the proposed approach, PSIM simulations, as well as experimental results are presented. The analysis was performed with a Interleaved Boost with Voltage Multiplier (IBVM) converter. Finally, the proposed approach is shown to be an alternative to the classical scanning methods or to the conventional solution of differential equations.

Keywords: Grey box modelling, Frequency domain identification, Continuous time system estimation
Abstract: This paper addresses parameter estimation problem of Continuous-/Discrete-Time (CT/DT) Linear Time-Invariant (LTI) systems, whose gain properties should satisfy given constraints in a priori specified frequencies, using measured data. The following are supposed in our problem: i) only input matrix has parameters to be estimated; ii) the state and the input are both measured, and the derivative of the state is also measured in CT case, and iii) the gain constraints in specified frequency ranges are given beforehand. Under these suppositions, a formulation to minimize the difference between the measured state derivative and the expected state derivative (in CT case) or the difference between the measured one-step-ahead state and the expected one-step-ahead state (in DT case) in Euclidean norm with the supposed gain constraints satisfied is given in terms of Linear Matrix Inequality (LMI). The effectiveness of the proposed method is demonstrated by an academic example in DT case as well as flight data obtained by JAXA's airplane in CT case.

Keywords: Input and excitation design, Continuous time system estimation, Stability and stabilization of hybrid systems
Abstract: The Minimum Phase (MP) properties of linear control systems can be reflected by its zero stability. The stability of zeros affects the system control performance. When a continuous-time system is discretized to a discrete-time system, the discretization process may render continuous-time system models have nonminimum phase. This paper analyses the MP properties of system and deduces a new stable condition of the zeros when continuous-time system is discretized by Forward Triangle Sample and Hold (FTSH) for sufficiently small sampling periods. Finally, two numerical examples have verified our results.

Keywords: Machine learning, Continuous time system estimation
Abstract: This paper is devoted to the application of a simple machine learning technique for the design of a receding horizon state observer. The proposed approach is based on a neural network trained to learn the inverse problem consisting in deriving the current system state from past measurements and inputs. The training data is obtained from simple integrations of the system dynamics to be observed. The approach is here applied to the problem of estimating the car density on a highway online. A comparison with the solution of an receding horizon observer based on an adjoint method and used as reference demonstrates the effectiveness of the proposed approach.

Keywords: Model formulation, experiment design, Identification and validation, Developments in measurement, signal processing
Abstract: Robust experimental design (RED) of sampling time scheduling has been discussed for parametric uncertain systems. Four RED methods, i.e., the pseudo-Bayesian design, the maximin design, the expectation-variance design, and the online experimental redesign, are investigated under the framework of model-based optimal experimental design (OED). Both the D-optimal and the E-optimal criteria are used as performance metrics. Two numerical procedures, the Powell's method and the semi-definite programming (SDP), are employed to obtain the optimum solution for REDs. The robustness performance of the four REDs are compared using a benchmark enzyme reaction system. In comparison to a typical uniform sampling strategy, the sampling time profiles from REDs are more focused on regions where the dynamic system has higher parametric sensitivities, indicating choice of informative data for parameter identification. The designed sampling strategies are also assessed by bootstrap parameter estimation with randomly generated initial points, where the difference between REDs can be observed.

Keywords: Digital implementation, Stability of nonlinear systems, Application of nonlinear analysis and design
Abstract: As the main contribution, this document provides a consistent discretization of a class of fixed-time stable systems, namely predefined-time stable systems. In the unperturbed case, the proposed approach allows obtaining not only a consistent but exact discretization of the considered class of predefined-time stable systems, whereas in the perturbed case, the consistent discretization preserves the predefined-time stability property. All the results are validated through simulations and compared with the conventional explicit Euler scheme, highlighting the advantages of this proposal.

Keywords: Fault detection and diagnosis
Abstract: This paper proposes a generalized minimum detectable fault (MDF) computation method based on the set-separation condition between the healthy and faulty residual sets for discrete-time linear parameter varying (LPV) systems with bounded inputs and uncertainties. First, we equivalently transform the multiple multiplicative actuator faults into the form of multiple additive actuator faults, which is benecial to simplify the problem. Then, by considering the 1-norm of the fault vector, we define the generalized MDF in the case of multiple additive actuator faults, which can be computed via solving a simple linear programming (LP) problem. Moreover, an analysis of the effect of the input vector on the magnitude of the generalized MDF is made. Since the proposed generalized MDF computation method is robust by considering the bounds of inputs and uncertainties, robust fault detection (FD) can be guaranteed whenever the sum of the magnitudes of all occurred faults is larger than the magnitude of the generalized MDF. At the end of this paper, a numerical example is used to illustrate the effectiveness of the proposed method.

Keywords: Fault detection and diagnosis
Abstract: This paper presents a real-time prediction method for fatigue damage of steam turbine. The temperature data and thermal stress data of the key parts are extracted by calculating the temperature field and the stress field. The composite stress is calculated according to the fourth strength theory, and the measured stress data are normalized. Support vector regression model is established, input and output data are trained and predicted. The relationship between stress and damage function is analyzed and fitted, and the framework of the real time fatigue damage prediction system is established. In the end, the effectiveness of the method is verified by simulation experiment.

Keywords: Fault detection and diagnosis
Abstract: This paper proposes a probabilistic robust parity relation based approach to fault detection of stochastic linear systems. Instead of assuming exact knowledge of disturbance distribution, the uncertainty of distribution information is taken into account by considering an ambiguity set of disturbance distributions. The biased minimax probability machine scheme is exploited to formulate an integrated design of the parity vector/matrix and the detection threshold. It maximizes the worst-case fault detection rate (FDR) with respect to selected reference faults, while ensuring a predefined worst-case false alarm rate. Firstly, a scalar residual design is derived in an analytical form. The analysis of its FDR in the presence of an arbitrary fault shows its limitation due to using a single reference fault. This issue is further addressed by proposing a vector residual design with a systematic method to select multiple reference faults. The efficacy of the proposed approach is illustrated by a simulation example.

Keywords: Fault detection and diagnosis
Abstract: In this paper, a method of distributionally robust fault detection (FD) is proposed for stochastic linear discrete-time systems by using the kernel density estimation (KDE) technique. For this purpose, an H₂ optimization-based fault detection filter is constructed for residual generation. Towards maximizing the fault detection rate (FDR) for a prescribed false alarm rate (FAR), the residual evaluation issue regarding the design of residual evaluation function and threshold is formulated as a distributionally robust optimization problem, wherein the so-called confidence sets are constituted to model the ambiguity of distribution knowledge of residuals in fault-free and faulty cases. A KDE based solution, robust to the estimation errors in probability distribution of residual caused by the finite number of samples, is further developed to address the targeting problem such that the residual evaluation function, threshold as well as the lower bound of FDR can be achieved simultaneously. A case study on a vehicle lateral control system demonstrates the applicability of the proposed FD method.

Keywords: Fault detection and diagnosis
Abstract: In this paper a method for fault detection and identification of affine input nonlinear systems is presented, which is based on derivative estimation with orthonormal Jacobi polynomials. A systematic approach is presented to derive a residual and a differential algebraic expression of the fault from the system description, which solely depends on measurable input and output signals as well as on their time derivatives. For this, a systematic algorithm is provided, which can be directly implemented in computer algebra packages. Furthermore, arbitrary disturbances are taken into account, by making use of a disturbance decoupling. Fault detection and identification is then achieved by polynomial approximation of the determined fault or residual expression. The results are illustrated for a faulty point-mass satellite model.

Keywords: Fault detection and diagnosis
Abstract: Monitoring of industrial systems for anomalies such as faults and cyber-attacks as unknown and extremely undesirable inputs in the presence of other inputs (like disturbances) is an important issue for ensuring the safety and the reliability of their operation. In this study, a robust anomaly detection filter is proposed for continuous linear Roesser systems using dynamic observer framework. Sufficient conditions for the existence of the observer and its sensitivity to anomaly as well as its robustness to disturbances are addressed via linear matrix inequalities (LMIs). The mentioned sensitivity and robustness are based on the H_- and H_infty performance indices, respectively. Finally, the performance of the proposed observer is demonstrated through a numerical example.

Keywords: Fault detection and diagnosis
Abstract: We propose a novel probabilistic fault detection scheme with adjustable reliability estimates. Our scheme consists of two phase, the first is the modelling phase, where a probabilistic fault detection design is devised, while the second is the validation phase, where reliability estimates of the design are adjusted online according to new operation records of the plant and the validated reliability. The modelling phase is based on two methods: residual generation, such as parity space, which is an important tool in fault detection problem, and scenario approach, which is a seminal trick to transfer intractable optimization problem into approximate tractable optimization problem and ensure reliability guarantees. The validation phase leverages the state-of-art posteriori probabilistic bounds of convex scenario programs with validation tests. Such a holistic design-and-validate scheme will can help technicians to make better decision. The efficacy of the proposed approach is illustrated on a simulated case study

Keywords: Fault detection and diagnosis, Adaptive observer design, Estimation and filtering
Abstract: An open-circuit fault-detection strategy is here proposed for single-phase DC/AC conversion. The power converter under consideration consists of an H-bridge and a capacitor with parallel resistance and current source in its DC side-these last two stand for the unknown system load and energy injection from renewable resources, respectively. An inductor filter is also included as a coupling element to the AC network. When an open-circuit fault occurs in the H-bridge, the resulting AC output waveform is asymmetric, and induces DC and harmonic components to the network. Hence, by using an additive fault modeling, the fault signature can be expressed by a constant term f_dc and a fluctuating signal. The sign of f_dc allows to determine the pair of faulty switches in the H-bridge. In this work, an DREM-based identification scheme is proposed to estimate f_dc. Through the sign of its estimate, it is possible to detect the pair of faulty switches. To assess our approaches, simulation results are included.

Keywords: Fault detection and diagnosis, Adaptive observer design, Mechanical and aerospace estimation
Abstract: This paper presents a robust actuator fault diagnosis algorithm for hexacopter Unmanned Aerial Vehicles (UAVs). The algorithm, based on Adaptive eXogenous Kalman Filter (AXKF), consists of two-stage operations: (i) a nonlinear observer and (ii) a linearized adaptive Kalman filter. To this end, we provide a sufficient condition for the nonlinear observer and recursive formulas for the linearized adaptive Kalman filter. The algorithm is tested for actuator fault diagnosis of a hexacopter UAV. Simulation results show that the proposed cascaded algorithm is able to accurately estimate the magnitude of the actuator fault.

Keywords: Fault detection and diagnosis, Distributed control and estimation, Sensor networks
Abstract: This paper studies the distributed fault detection problem for linear time-invariant (LTI) systems with distributed measurement output. A distributed H−/L∞ fault detection observer (DFDO) design method is proposed to detect actuator faults of the monitored system in the presence of a bounded process disturbances. The DFDO consists of a network of local fault detection observers, which communicate with their neighbors as prescribed by a given network graph. By using finite-frequency H− performance, the residual in fault detection is sensitive to fault in the interested frequency-domain. The residual is robust against effects of the external process disturbance by L∞ analysis. A systematic algorithm for DFDO design is addressed and the residual thresholds are calculated in our distributed fault detection scheme. Finally, we use a numerical simulation to demonstrate the effectiveness of the proposed distributed fault detection approach.

Keywords: Fault detection and diagnosis, Estimation and filtering
Abstract: In this paper, the problem of intermittent fault detection is investigated for nonlinear stochastic systems. The moving horizon estimation with dynamic weight matrices is proposed, where the weight matrices are adjusted by an unreliability index of prior estimate to avoid the smearing effects of intermittent faults. Based on the particle swarm optimization algorithm, the nonlinear optimization problem is solved and the approximate estimate is derived. Finally, the feasibility and effectiveness of the proposed algorithm are validated by a numerical example.

Keywords: Fault detection and diagnosis, Estimation and filtering
Abstract: Offshore wind turbines suffer from asymmetrical blade loading, resulting in enhanced structural fatigue. Individual pitch control (IPC) is an effective method to achieve blade load mitigation, accompanied by enhancing the pitch movements and thus increased the probability of pitch actuator faults. The occurrence of faults will deteriorate the IPC load mitigation performance, which requires fault-tolerant control (FTC). IPC is itself analogous to the FTC problem because the action of rotor bending can be considered as a fault effect. Therefore, the work thus proposes a "co-design" strategy, constituting a combination of IPC-based asymmetrical load mitigation combined with FTC acting at the pitch system level. The FTC uses the well-known fault estimation and compensation strategy. A Proportional-Integral PI-based IPC strategy for blade mitigation is proposed in which the robust fault estimation is achieved using a robust unknown input observer (UIO). The performance of two pitch controllers (baseline pitch controller, PI-based IPC) are compared in the presence of pitch actuator faults (including low pressure & loss of effectiveness). The effectiveness of the proposed strategy is verified on the 5MW NREL wind turbine system.

Keywords: Fault detection and diagnosis, Frequency domain identification, Multi-agent systems
Abstract: In this paper, we propose a method to identify the damaged component and quantify its damage amount in a large network given its overall frequency response. The identification procedure takes advantage of our previous work which exactly models the frequency response of that large network when it is damaged. As a result, the test shows that our method works well when some noise present in the frequency response measurement. In addition, the effects brought by a damaged component which is located deep inside that large network are also discussed.

Keywords: Fault detection and diagnosis, Grey box modelling, Channel estimation/equalisation
Abstract: This paper addresses the problem of change detection for a quadcopter in the presence of wind disturbances. Different aspects of the quadcopter dynamics and various flight conditions have been investigated. First, the wind is modeled using the Dryden wind model as a sum of a low-frequent and a turbulent part. Since the closed-loop control can compensate for system changes and disturbances and the effect of the wind disturbance is significant, the residuals obtained from a standard simulation model can be misleading. Instead, a sensor-to-sensor submodel of the quadcopter is selected to detect a change in the payload using the Instrumental Variables (IV) cost function. It is shown that the mass variation can be detected using the IV cost function in different flight scenarios.

Keywords: Fault detection and diagnosis, Identifiability, Filtering and smoothing
Abstract: This paper presents a rigorous definition of the isolability of a fault in a flat system whose flat outputs are measured by sensors that are subject to faults. In particular, if only one sensor or actuator is faulty at a time, we show that the isolation of faults can be achieved if a pair of flat outputs satisfies some independence condition. A detailed characterization of this condition is presented. Finally, the pertinence of the isolability concept is demonstrated on the example of a three tank system.

Keywords: Fault detection and diagnosis, LPV system identification, Stability and stabilization of hybrid systems
Abstract: This paper proposes a mixed active/passive robust fault detection and isolation (FDI) method for discrete-time linear paramter varying (LPV) systems based on set-theoretic unknown input observers (SUIO) and invariant sets. The robustness against system uncertainties (i.e., process disturbances, measurement noises and so on) in FDI of LPV systems can be guaranteed by actively decoupling or passively bounding their effect on residual signal. Furthermore, the quadratic H1 stability condition of the LPV-form state-estimation-error dynamics is established based on a group of linear matrix inequalities (LMIs). Under the precondition of stability, a family of residual sets are constructed to establish set-separation guaranteed fault isolation (FI) conditions using invariant sets off-line. As long as the occurred faults satisfy the guaranteed FI conditions, they can be isolated from each other. At the end, a numerical example is used to illustrate the effectiveness of the proposed method.

Keywords: Fault detection and diagnosis, Machine learning, Grey box modelling
Abstract: Development of model-based fault diagnosis methods is a challenge when industrial systems are large and exhibit complex process behavior. Latent projection (LP), a statistical method that extract features of data via dimensionality reduction, is an alternative approach to diagnosis as it can be formulated to not rely on process knowledge. However, LP methods may perform poorly at identifying abnormal process variables due a "fault smearing" effect - variables unaffected by a fault are unintentionally characterized as being abnormal. The effect occurs because data compression permits faulty and non-faulty variables to interact. This paper presents an autoencoder (AE), a nonlinear LP method based on neural networks, as a monitoring method of a simulated nonlinear triple tank process (TTP). Simulated process data was used to train the AE to generate a monitoring statistic representing the condition of the TTP. Sparsity was introduced in the AE to reduce variable interactivity. The AE's ability to detect a fault was demonstrated. The individual contributions of process variables to the AE's monitoring statistic were analyzed to reveal the process variables that were no longer consistent with normal operating conditions. The key result in this study was that sparsity reduced fault smearing onto unaffected variables and increased the contributions of actual faulty variables.

Keywords: Fault detection and diagnosis, Machine learning, Time series modelling
Abstract: Toothed belt drives are used in manifold automation applications. But only if the belt tension is properly adjusted, optimal working conditions are ensured. A loss of efficiency or even breakdowns might be the consequences otherwise. For this reason, tension monitoring reduces operation costs and may prevent failures. In order to meet industrial requirements, the monitoring is supposed to rely on standard sensor data. From this data, features are extracted in time and frequency domain which are passed on to a random forest. For further improvement, a segmentation of the frequency spectrum is performed beforehand. In this way, interval-based spectral features can be extracted to capture small distinctive parts in the frequency domain. For this purpose, two different segmentation procedures are compared in a random forest regression. A belt drive powered by a 1.9 kW synchronous servomotor is used to evaluate the proposed approaches in two different industrial scenarios. The experimental results show that both segmentation methods enhance the performance of a tree-based regression and offer a reliable tension prediction.

Keywords: Fault detection and diagnosis, Mechanical and aerospace estimation
Abstract: Actuation failure is one of the causes of loss of control in-flight accidents. Aircraft usually have multiple redundant actuators to mitigate failures, and Failure Detection and Isolation Systems (FDIS) are used to diagnose failures and reconfigure software/hardware to enhance safety. However, the large number of redundant actuators interferes with the FDIS. To detect and isolate failures in fixed-wing aircraft with redundant actuators, this work proposes the combined use of two different strategies of the Two-Stage Kalman Filter. A Supervisory Loop is included using heuristics and statistics to diagnose the actuators, and a Feed-Forward Differential is implemented to improve the isolation process without interfering with the aircraft flight. The solution is evaluated in the detection of an aileron failure in a Boeing 747 simulator.

Keywords: Fault detection and diagnosis, Nonlinear system identification
Abstract: The problem of sensor fault diagnosis in technical systems described by nonlinear dynamic models is considered. To address the problem, sliding mode observers are used. The suggested approach for constructing sliding mode observers is based on the reduced order model of the initial system. This allows to reduce complexity of sliding mode observers and relax the limitations imposed on the initial system.

Keywords: Fault detection and diagnosis, Particle filtering/Monte Carlo methods, Diagnosis of discrete event and hybrid systems
Abstract: Sensor or actuator faults occurring on a Unmanned Aerial Vehicle (UAV) can compromise the system integrity. Fault diagnosis methods is then becoming a required feature for those systems. In this paper, the focus is on fault estimation for a fixed-wing UAVs in the presence of simultaneous sensor faults. The altitude measurements of a UAV are commonly obtained from the combination of two different types of sensors: a Global Navigation Satellite System (GNSS) receiver and a barometer. Both sensors are subject to additive abrupt faults. To deal with the multimodal nature of the faulty modes, a Jump-Markov Regularized Particle Filter (JMRPF) is proposed in this paper to estimate the barometric altitude and GNSS altitude measurement faults, including the case when both faults occur simultaneously. This method is based on a regularization step that improves the robustness thanks to the approximation of the conditional density by a kernel mixture. In addition, the new jump strategy estimates the correct failure mode in 100% of the 100 simulations performed in this paper. This approach is compared with an Interacting Multiple Model Kalman Filter (IMM-KF) and the results show that the JMRPF outperforms the IMM-KF approach, particularly in the ambiguous case when both sensors are simultaneously subject to additive abrupt faults.

Keywords: Fault detection and diagnosis, Particle filtering/Monte Carlo methods, Randomized methods
Abstract: The satellite sea surface temperature (SST) measurement is based on the detection of ocean radiation using microwave or infrared wavelengths within the electromagnetic spectrum. The radiance of individual wavelengths can be converted into brightness temperatures for using in SST determination. The calibration and validation of the determined SST data require reference measurements from in-situ observations. These in-situ observations are from various platforms such as ships, drifters, floats and mooring buoys and require a high measurement accuracy. This paper presents an investigation about the possibility of using a glider as possible in-situ platform. A glider is a type of autonomous underwater vehicle (AUV) which can log oceanographic data over a period of up to one year by following predetermined routes. In contrast to buoys, a glider allows a targeted investigation of regional anomalies in SST circulations. To assess the quality of SST observations from a glider, logged data from a glider mission in the Atlantic Ocean from 2018 to 2019 and corresponding satellite SST data were used. The influence of variables (e.g. measurement depth, latitude, view zenith angle, local solar time) of the bias between satellite and glider SST data was investigated using sensitivity analysis. A new and efficient distribution-based method for global sensitivity analyzes, called PAWN, was used successfully. Interested readers will find information about its operation principle and the usage for passive observations where only ``given-data'' are available.

Keywords: Fault detection and diagnosis, Secure networked control systems
Abstract: This paper deals with a topology for a class of interconnected systems, referred to as a highly interconnected system, consisting of interconnected plants and local controllers. We address the respective cyber attack surfaces as well as a design approach for detection and isolation of covert cyber attacks. For each pair of plant and controller, a cyber attack is implemented by a malicious agent, and its detection and isolation are achieved by associating the controller with two observers. These observers estimate the states of the plant, and compare the estimated states to determine if a neighbouring plant is under a covert cyber attack. The paper presents the modelling of the topology, the analysis of the covertness of cyber attacks, the design approach for the detection and isolation as well as a required existence condition. Simulation results are provided for the application of the design approach to interconnected pendula systems that are subject to a covert cyber attack.

Keywords: Fault detection and diagnosis, Sensor networks, Estimation and filtering
Abstract: This paper is concerned with the distributed fault diagnosis problem for a class of time-varying systems over sensor networks with nonlinearity and uncertainty. For the purpose of solving the problem of data conflict, the stochastic protocol is used to determine which node has the right to send data to the estimator at a certain transmission time. The aim of this paper is to design a set of distributed estimators to detect, isolate and estimate fault signals. The upper bound of estimation error covariance is obtained by solving two recursive matrix equations and the upper bound can be minimized by designing appropriate estimator gain at each step. Finally, a numerical example is provided to show the effectiveness of the proposed design scheme.

Keywords: Fault detection and diagnosis, Stochastic system identification, Synthesis of stochastic systems
Abstract: This paper deals with a proactive maintenance strategy used to increase the reliability of equipment. A predicting schedule of the renewal interventions will be proposed so as to ensure optimal maintenance for the equipment. Hence, the goal is to find the optimal time which is the most profitable to carry out the equipment renewal operations. The deterioration process is modeled by Markov chains, which is capable to provide information about the tendency of the equipment state. For the optimization of the maintenance a preventive strategy based on the average maintenance cost was used. The minimum maintenance average cost corresponds to the optimal time when it is most efficient to stop the equipment operation and to renew it.

Keywords: Fault detection and diagnosis, Time series modelling, Machine learning
Abstract: Fault diagnosis is essential to ensure the operation security and economic efficiency of the chemical system. Many fault diagnosis methods have been designed for the chemical process, but most of them ignore the temporal correlation in the sequential observation signals of the chemical process. A novel deep learning method based on Stacked Long Short-Term Memory (LSTM) neural network is proposed, which can effectively model sequential data and detect the abnormal values. The proposed method is also able to fully exploit the long-term dependencies information in raw data and adaptively extract the representative features. The dataset of Tennessee Eastman (TE) process is utilized to verify the practicability and superiority of the proposed method. Extensive experimental results show that the fault detection and diagnosis model we proposed has an excellent performance when compared with several state-of-the-art baseline methods.

Keywords: Fault detection and diagnosis, Time series modelling, Mechanical and aerospace estimation
Abstract: Accelerated degradation testing (ADT) is used to efficiently assess the reliability and lifetime of a high reliable products under normal stress. In general, it is common in practice to build stochastic models of degradation under a single failure mechanism based on the ADT data. However, in real applications, multi-failure mechanisms may influence the degradation process. Motivated by this, a mixed stochastic process model for ADT is proposed in this paper. The mixed stochastic process combines two singlestochastic processes with weights determined by a quantitative method that establishes the relationship with accelerated stress. After the unknown parameter estimation, the proposed model under normal stress level can be obtained. The results show that the proposed model can be used for ADT modeling under multi-failure mechanisms.

Keywords: Fault detection and diagnosis, Time series modelling, Recursive identification
Abstract: Condition monitoring of electric motor driven mechanisms is of great importance in industrial machines. The knowledge of the actual health state of such components permits to address maintenance policies which results in better exploitation of their actual operational life span and consequently in maintenance cost reduction. In this paper, we exploit the way electric cams are implemented on the vast majority of PLC/Motion controllers to develop a suitable condition monitoring procedure. This technique relies on computing the higher-order differences of the current absorbed by slave motors to get signals that do not depend on a priori knowledge of the cam trajectory and of the mechanism nominal model. Subsequently, we will use these data in the Model-of-Signals framework, to gather information on the mechanism's health condition, which in turn can be used to perform predictive maintenance policies. The differenced signal is modelled as an ARMA process and the model capabilities in condition monitoring are then shown in simulation and experimental application. Besides, this framework allows exploiting the edge-computing capabilities of the machinery controllers by implementing recursive estimation algorithms.

Keywords: Closed loop identification, Fault detection and diagnosis, Diagnosis of discrete event and hybrid systems
Abstract: We present in this paper a timed discrete event model for system identification with the aim of fault detection, called Timed Automaton with Outputs and Conditional Transitions (TAOCT). The TAOCT is an extension of a recent untimed model proposed in the literature, called Deterministic Automaton with Outputs and Conditional Transitions (DAOCT). Differently from the DAOCT, where only the logical behavior of the discrete event system is considered, the TAOCT takes into account information about the time that the events are observed, and, for this reason, it can be used for the detection of faults that cannot be detected by using untimed models, such as faults that lead the fault detector to deadlocks. The TAOCT represents the fault-free system behavior, and a fault is detected when the observed behavior is different from the behavior predicted by the model, considering both logical and timing information. A practical example is used to illustrate the results of the paper.

Keywords: Mechanical and aerospace estimation, Bayesian methods, Fault detection and diagnosis
Abstract: In this paper, a damage assessment framework based on the infrared technology is proposed to assess the damage of the spacecraft. This framework mainly contains three steps. Firstly, a damage reconstruction model based on sparse model is proposed to reconstruct the damage image of different layers. To estimate the parameter of the model, variational Bayesian is used for calculating the parameters. Secondly, a damage extraction method is used to eliminate noise in the images. At the same time, this procedure can effectively make the weak subsurface damage more clear. Finally, in order to compare the location of surface and subsurface damage, image fusion method is used to achieve damage fusion. In the experiment, the proposed framework is used for the Whipple shield detection, both images and evaluation parameters show the effectiveness and high-accuracy of the new model.

Keywords: Mechanical and aerospace estimation, Fault detection and diagnosis, Stochastic hybrid systems
Abstract: In order to realize the automatic identification of pressure vessel defects, an improved adaptive defect recognition feature extraction algorithm through ECPT (Eddy current pulsed thermography) is proposed. The proposed feature extraction algorithm consists of five elements: thermal image data segmentation, variable interval search, probability density function modeling, data classification, and reconstructed image acquisition. The combination of data block selection and variable interval search can reduce the double counting. And the KG-EM (Kmeans-GMM-EM) algorithm is proposed to obtain the Gaussian mixture model corresponding to the classification, and thus the corresponding probability is obtained to classify the TTRs (Transient Thermal Response). The reconstructed thermal image is obtained by the classified TTRs. This method can extract the main information of the image accurately and efficiently. Experimental results are provided to demonstrate their effectiveness.

Keywords: Supervisory control and automata, Fault detection and diagnosis
Abstract: Wind turbines components are subject to considerable stresses and fatigue due to extreme environmental conditions to which are exposed, especially those located offshore. Interest in the integration of control with life estimation of components has increased in recent years. The integration of a systems health management module with MPC control provides the wind turbine a mechanism to operate safely and optimize the tradeoff between components life and energy production. In this paper, a health-aware LPV model predictive control approach for wind turbines is proposed. The proposed controller establish a trade-off between the economic objective based on maximizing the energy production but at the same time maximizing the remaining useful life. The controller uses an LPV model for dealing with the non-linearity of the wind turbine model. The proposed approach is tested on a well-known wind turbine case study.

Keywords: Machine learning, Fault detection and diagnosis, Mechanical and aerospace estimation
Abstract: Transitions from stable to unstable states occurring in dynamical systems can be sudden leading to catastrophic failure and huge revenue loss. For detecting these transitions during operation, it is of utmost importance to develop an accurate data-driven framework that is robust enough to classify stable and unstable scenarios. In this paper, we propose deep learning frameworks that show remarkable accuracy in the classification task of combustion instability on carefully designed diverse training and test sets. We train our model with data from a laboratory-scale combustion system showing stable and unstable states. The dataset is multimodal with correlated data of hi-speed video and acoustic signals. We develop a labeling mechanism for sequences by implementing Kullback–Leibler Divergence on the time-series data. We develop deep learning frameworks using 3D Convolutional Neural Network and Long Short Term Memory network for this classification task. To go beyond the accuracy and to gain insights into the predictions, we incorporate attention mechanism across the time-steps. This aids in understanding the time-periods which contribute significantly to the prediction outcome. We validate the insights from a domain knowledge perspective. By exploring inside the accurate black-box models, this framework can be used for the development of better detection frameworks in different dynamical systems.

Keywords: Fault Detection, Diagnosis, Identification, Isolation and Tolerance for Autonomous Vehicles, Modeling, supervision, control and diagnosis of automotive systems, Autonomous Vehicles
Abstract: Stealthy false data injection attacks on cyber-physical systems introduce erroneous measurements onto sensors with the intent to degrade system performance. An intelligent attacker can design stealthy attacks with knowledge of the system model and noise characteristics to evade detection from state-of-the-art fault detectors by remaining within detection thresholds. However, during these hidden attacks, an attacker with the intention of hijacking a system will leave traces of non-random behavior that contradict with the expectation of the system model. Given these premises, in this paper we propose a run-time monitor called Cumulative Sign (CUSIGN) detector, for identifying stealthy falsified measurements by identifying if measurements are no longer behaving in a random manner. Specifically, our proposed CUSIGN monitor considers the changes in sign of the measurement residuals and their expected occurrence in order to detect if a sensor could be compromised. Moreover, our detector is designed to be a memoryless procedure, eliminating the need to store large sequences of data for attack detection. We characterize the detection capabilities of the proposed CUSIGN technique following the well-known chi2 failure detection scheme. Additionally, we show the advantage of augmenting CUSIGN to the model-based Cumulative Sum (CUSUM) detector, which provides magnitude bounds on attacks, for enhanced detection of sensor spoofing attacks. Our approach is validated with simulations on an unmanned ground vehicle (UGV) during a navigation case study.

Keywords: Identification for control
Abstract: In this paper a Maximum Likelihood estimation algorithm for error-model modelling using a stochastic embedding approach is developed. The error-model distribution is approximated by a finite Gaussian mixture. An Expectation-Maximization based algorithm is proposed to estimate the nominal model and the distribution of the parameters of the error-model by using the data from independent experiments. The benefits of our proposal are illustrated via numerical simulations.

Keywords: Identification for control
Abstract: A new method for identification of ill-conditioned systems is suggested. Our aim is to provide a solution that is practical and functional in the sense that no initial knowledge about process is needed, light-weight tools can be used for identification (e.g. simple ARX models with standard least-squares regression), and model structures with minimal number of parameters and states are used. The main idea is to employ principal component analysis (PCA) to rotate the outputs before identifying the process in directions important for control.

Keywords: Identification for control, Closed loop identification, Experiment design
Abstract: The problem of accurate plasma shape control is significant, both for modern tokamaks, for example for the Globus-M/M2 spherical tokamak, and for future thermonuclear tokamak-reactors using magnetic plasma confinement. The article presents the new results of design and modeling the plasma shape control system for the Globus-M/M2 spherical tokamak with the pre-trained neural network as a plasma equilibrium reconstruction algorithm, which is included in the feedback of the system. To collect the necessary data for training the neural network the developed magnetic plasma evolutionary code was used.

Keywords: Errors in variables identification
Abstract: In this paper we address the problem of identifying a static errors-in-variables system. Our proposal is based on the Expectation-Maximization algorithm, in which we consider that the distribution of the noise-free input is approximated by a finite Gaussian mixture. This approach allows us to estimate the static system parameters, the input and output noise variances, and the Gaussian mixture parameters. We show the benefits of our proposal via numerical simulations.

Keywords: Identification for control, Nonlinear system identification, Time series modelling
Abstract: This paper proposes a data-driven immersion approach to obtain linear equivalents or approximations of discrete-time nonlinear systems. Exact linearization can only be achieved for very particular classes of systems. In general cases, we aim to obtain a finite-time linear approximation. Our approach only takes a finite set of trajectories and hence an analytic model is not required. The mismatch between the approximate linear model and the original system is concretely discussed with formal bounds. We also provide a Koopman-operator interpretation of this technique, which shows a link between system immersibility and the Koopman operator theory. Several numerical examples are taken to show the capabilities of the proposed immersion approach. Comparison is also made with other Koopman-based lifting approaches which use radial basis functions and monomials.

Keywords: Recursive identification, Identification for control, Discrete event modeling and simulation
Abstract: This paper presents a novel identification procedure for a class of hybrid dynamical systems. In particular, we consider hybrid dynamical systems which are single flowed and single jumped and whose flow and jump maps linearly depend on two sets of unknown parameters. A systematic way to determine whether the system is flowing or jumping is introduced and used to identify the unknown parameters by employing a linear recursive estimator. Simulations have been performed to prove the validity of the proposed methodology. Results proved the efficiency and accuracy of the developed identification procedure.

Keywords: Recursive identification, Identification for control, Time series modelling
Abstract: Fast convergent, accurate, computationally efficient, parallelizable, and robust matrix inversion and parameter estimation algorithms are required in many time-critical and accuracy-critical applications such as system identification, signal and image processing, network and big data analysis, machine learning and in many others. This paper introduces new composite power series expansion with optionally chosen rates (which can be calculated simultaneously on parallel units with different computational capacities) for further convergence rate improvement of high order Newton-Schulz iteration. New expansion was integrated into the Richardson iteration and resulted in significant convergence rate improvement. The improvement is quantified via explicit transient models for estimation errors and by simulations. In addition, the recursive and computationally efficient version of the combination of Richardson iteration and Newton-Schulz iteration with composite expansion is developed for simultaneous calculations. Moreover, unified factorization is developed in this paper in the form of tool-kit for power series expansion, which results in a new family of computationally efficient Newton-Schulz algorithms.

Keywords: Subspace methods, Closed loop identification, Identification for control
Abstract: This paper proposes an estimation method of the innovations model in closed loop environment by using the estimate of the innovations process. The estimate of the innovations process from the finite interval of data has a bias, so are the estimate of the proposed method. However, it is analyzed that the bias can be reduced. The Kalman gain and the covariance of the innovations process are estimated by using a semi-definite programming problem previously proposed by the authors. Numerical simulation illustrates the proposed method gives better performance than Closed-Loop MOESP and PBSID when the data length is large and the past horizon is selected low.

Keywords: Closed loop identification, Identification for control, Identifiability
Abstract: This paper presents a method of closed-loop identification for multivariable systems without external excitation. The method is specially designed for model predictive control (MPC) systems. Without using external excitation (test signals), the method ensures the informativity of the closed-loop data and, at the same time, improve the control performance during the test period. The purpose of the study is to reduce the cost of identification test. The basic idea is to switch the input weighting matrix in the MPC controller which leads to the informativity of the data-set. A preliminary test is carried out in order to find a new input weighting matrix which improve the control performance; then a switching scheme is developed based on the two weighting matrixes. Traditional simulation based model validation no longer works in closed-loop identification without excitation, and model error bounds on the frequency responses can be used instead. The effectiveness of the proposed method is demonstrated by a simulation study.

Keywords: Errors in variables identification
Abstract: This paper deals with the identification of FIR models corrupted by white input noise and colored output noise. An identification algorithm that exploits the properties of both the dynamic Frisch scheme and the high-order Yule-Walker (HOYW) equations is proposed. It is shown how the HOYW equations allow defining a selection criterion for identifying the input noise variance (and then the FIR coefficients) within the Frisch locus of solutions. The proposed approach does not require any a priori knowledge about the input and output noise variances. The algorithm performance is assessed by means of Monte Carlo simulations.

Keywords: Errors in variables identification, Frequency domain identification
Abstract: Several estimation methods have been proposed for identifying errors-in-variables systems, where both input and output measurements are corrupted by noise. One of the more interesting approaches is the Frisch scheme. The method can be applied using either time or frequency domain representations. This paper investigates the general mathematical and geometrical aspects of the Frisch scheme, illustrating the analogies and the differences between the time and frequency domain formulations.

Keywords: Errors in variables identification, Frequency domain identification, Channel estimation/equalisation
Abstract: This paper describes a new approach for the blind identification of a two-channel FIR system from a finite number of output measurements, in the presence of additive and uncorrelated white noise. The proposed approach is based on frequency domain data and, as a major novelty, it enables the estimation to be frequency selective. The features of the proposed method are analyzed by means of Monte Carlo simulations. The benefits of filtering the data and using only part of the frequency domain is highlighted by means of a numerical example.

Keywords: Subspace methods
Abstract: This paper presents a subsystem decoupling method for Linear Time Invariant Discrete-time systems. The aim is to control a selected subsystem, while not affecting the remaining dynamics. The paper extends earlier continuous time results to discrete time systems over a finite frequency interval. Decoupling is achieved by suitable input and output blend vectors, such that they maximize the sensitivity of the selected subsystem, while at the same time they minimize the transfer through the undesired dynamics. The proposed algorithm is based on an optimization problem involving Linear Matrix Inequalities, where the H minus index of the controlled subsystem is maximized, while the transfer through the dynamics to be decoupled is minimized by a sparsity like criteria. The present approach has the advantage that it is directly applicable to stable and unstable subsystems also. Numerical examples demonstrate the effectiveness of the method.

Keywords: Subspace methods, Stability and stabilization of hybrid systems
Abstract: In this study, we give necessary and sufficient conditions for well posedness of Conewise Linear Systems in 3-dimensional space where the vector field is allowed to be discontinuous. The conditions are stated using the subspaces derived from subsystem matrices and the results are compared with the existing conditions given in the literature. We show that even we don’t have a fixed structure on system matrices as in bimodal systems, similar subspaces and numbers again determines well posedness.

Keywords: Subspace methods, Vibration and modal analysis
Abstract: The transfer function of a linear system is defined in terms of the quadruplet of matrices (A,B,C,D) that can be identified from input and output measurements. Similarly these matrices determine the state space evolution for the considered dynamical system. Estimation of the quadruplet has been well studied in the literature from both theoretical and practical points of view. Nonetheless, the uncertainty quantification of their estimation errors has been mainly discussed from a theoretical viewpoint. For several output-only and input/output subspace methods, the variance of the (A,C) matrices can be effectively obtained with recently developed first-order perturbation-based schemes. This paper addresses the estimation of the (B,D) matrices, and the remaining problem of the effective variance computation of their estimates and the resulting transfer function. The proposed schemes are validated on a simulation of a mechanical system.

Keywords: Frequency domain identification, Filtering and smoothing, Channel estimation/equalisation
Abstract: A closed-form Laguerre-domain representation of discrete linear time-invariant systems with constant input time delay is derived. It is shown to be useful in a l_2 to l_2 system identification setup (with l_2 denoting square-summables signals) often arising in biomedical applications, where the experimental protocol does not allow for persistent excitation of the system dynamics. The utility of the proposed system representation is demonstrated on a problem of drug kinetics estimation from clinical data.

Keywords: Learning for control
Abstract: In this paper, online convex optimization is applied to the problem of controlling linear dynamical systems. An algorithm similar to online gradient descent, which can handle time-varying and unknown cost functions, is proposed. Then, performance guarantees are derived in terms of regret analysis. We show that the proposed control scheme achieves sublinear regret if the variation of the cost functions is sublinear. In addition, as a special case, the system converges to the optimal equilibrium if the cost functions are invariant after some finite time. Finally, the performance of the resulting closed loop is illustrated by numerical simulations.

Keywords: Learning for control, Bounded error identification, Identification for control
Abstract: For the analysis, simulation, and controller design of large-scale systems, a surrogate model is mostly required. The surrogate model should have small complexity while it approximates precisely the system behaviour with a bound on the error. A standard approach to compute a reduced model is given by modelling the system and applying model order reduction techniques. Contrary, we propose a data-driven approach. Hence, we derive a surrogate model of the input-output behaviour of LTI systems without knowledge of a model. Moreover, a bound on the maximal error between the system and the surrogate model is obtained. We analyse the stability and convergence of the presented schemes and we apply them on a benchmark system from the model-order-reduction literature.

Keywords: Learning for control, Identification for control, Experiment design
Abstract: This paper presents a novel approach to synthesize dual controllers for unknown linear time-invariant systems with the tasks of optimizing a quadratic cost while reducing the uncertainty. To this end, a synthesis problem is defined where the feedback law has to simultaneously gain knowledge of the system and robustly optimize the cost. By framing the problem in a finite horizon setting, the trade-offs arising when the tasks include both identification and control are formally captured in the optimization problem. Results show that efficient exploration strategies are achieved when the structure of the problem is exploited.

Keywords: Learning for control, Machine learning, Bounded error identification
Abstract: We propose a non-parametric regression methodology that enforces the regressor to be fully consistent with the sample set and the ground-truth regularity assumptions. As opposed to the Nonlinear Set Membership technique, this constraint guarantees the attainment of everywhere differentiable surrogate models, which are more suitable to optimization-based controllers that heavily rely on gradient computations. The presented approach is named Smooth Lipschitz Regression (SLR) and provides error bounds on the prediction error at unseen points in the space. A numerical example is given to show the effectiveness of this method when compared to the other alternatives in a Model Predictive Control setting.

Keywords: Learning for control, Machine learning, Grey box modelling
Abstract: Many control tasks can be formulated as tracking problems of a known or unknown reference signal. Examples are motion compensation in collaborative robotics, the synchronisation of oscillations for power systems or the reference tracking of recipes in chemical process operation. Both the tracking performance and the stability of the closed-loop system depend strongly on two factors: Firstly, they depend on whether the future reference signal required for tracking is known, and secondly, whether the system can track the reference at all. This paper shows how to use machine learning, i.e. Gaussian processes, to learn a reference from (noisy) data while guaranteeing trackability of the modified desired reference predictions within the framework of model predictive control. Guarantees are provided by adjusting the hyperparameters via a constrained optimisation. Two specific scenarios, i.e. asymptotically constant and periodic references, are discussed.

Keywords: Learning for control, Machine learning, Nonparametric methods
Abstract: A framework that is becoming particularly appealing to design control algorithms is that of devising the control policy from examples (or demonstrations). At their roots these control from demonstration techniques, which are gaining considerable attention under the label of Inverse Reinforcement Learning (IRL), rely on Inverse Optimal Control and Optimization. Today, IRL/control is recognized as an appealing framework to learn policies from success stories and potential applications include planning and preferences/prescriptions learning. There is then no surprise that, over the years, a number of techniques have been developed to address the problem of devising control policies from demonstrations, mainly in the context of Markov Decision Processes (MDPs). In this extended abstract we introduce an approach to synthesize control policies from examples. This approach formalizes the control problem as an optimization problem where the Kullback-Leibler Divergence between an ideal probability density function (pdf, obtained from e.g. demonstrations) and the pdf modeling the system/plant is minimized. A key technical novelty of our results lies in the fact that we explicitly embed actuation constraints in our formulation, thus solving an optimization problem where the Kullback-Leibler Divergence is minimized subject to constraints on the control variable. One of the main advantages of our results over classic Inverse Reinforcement Learning (Inverse Control) approaches is that policies can be synthesized from data without requiring that the system is a MDP. Moreover, by embedding actuation constraints into the problem formulation and by solving the resulting optimization, we can export the policy that has been learned on other systems that have different actuation capabilities. As an additional contribution, we devise from our theoretical results an algorithmic procedure. The key reference applications over which the algorithm was tested involved an autonomous driving use case and full results will be presented at the conference.

Keywords: Learning for control, Nonparametric methods, Identification for control
Abstract: A non-parametric technique for modeling of systems with unknown nonlinear Lipschitz dynamics is presented. The key idea is to successively utilize measurements to approximate the graph of the state-update function of the system dynamics using envelopes described by quadratic constraints. The proposed approach is then used for computing outer approximations of the state-update function using convex optimization. We highlight the efficacy of the proposed approach via a detailed numerical example.

Keywords: Machine learning, Learning for control, Bayesian methods
Abstract: Although machine learning is increasingly applied in control approaches, only few methods guarantee certifiable safety, which is necessary for real world applications. These approaches typically rely on well-understood learning algorithms, which allow formal theoretical analysis. Gaussian process regression is a prominent example among those methods, which attracts growing attention due to its strong Bayesian foundations. Even though many problems regarding the analysis of Gaussian processes have a similar structure, specific approaches are typically tailored for them individually, without strong focus on computational efficiency. Thereby, the practical applicability and performance of these approaches is limited. In order to overcome this issue, we propose a novel framework called GP3, general purpose computation on graphics processing units for Gaussian processes, which allows to solve many of the existing problems efficiently. By employing interval analysis, local Lipschitz constants are computed in order to extend properties verified on a grid to continuous state spaces. Since the computation is completely parallelizable, the computational benefits of GPU processing are exploited in combination with multi-resolution sampling in order to allow high resolution analysis.

Keywords: LPV system identification, Experiment design, Machine learning
Abstract: Active learning is proposed for selection of the next operating points in the design of experiments, for identifying linear parameter-varying systems. We extend existing approaches found in literature to multiple-input multiple-output systems with a multivariate scheduling parameter. Our approach is based on exploiting the probabilistic features of Gaussian process regression to quantify the overall model uncertainty across locally identified models. This results in a flexible framework which accommodates for various techniques to be applied for estimation of local linear models and their corresponding uncertainty. We perform active learning in application to the identification of a diesel engine air-path model, and demonstrate that measures of model uncertainty can be successfully reduced using the proposed framework.

Keywords: Machine learning, Randomized methods
Abstract: In this paper the problem of a multidimensional optimization in unsupervised learning and clustering is studied under significant uncertainties in the data model and measurements of penalty functions. We propose a modified version of SPSA-based algorithm which maintains stability under conditions such as a sparse Gaussian mixture model. This data model is important because it can be effectively used to evaluate the noise model in many practical systems. The proposed algorithm is robust to external disturbances and is able to process data sequentially, ``on the fly''. In this paper provides a study of this algorithm and its mathematical justification. The behavior of the algorithm is illustrated by examples of its use for clustering in various difficult conditions.

Keywords: Frequency domain identification, Machine learning, Nonparametric methods
Abstract: Linear time-varying systems are a class of systems, the dynamics of which evolve in time. This results in a time-varying transfer function where each frequency has a time-varying gain. In classical identification techniques, basis functions are employed to fit these time-varying gains. In this paper a new method based on Gaussian process regression is presented. The advantage of the proposed method is a more convenient model structure and model order selection.

Keywords: Machine learning, Stochastic system identification, Particle filtering/Monte Carlo methods
Abstract: Although machine learning techniques are increasingly employed in control tasks, few methods exist to predict the behavior of closed-loop learning-based systems. In this paper, we introduce a method for computing confidence regions of closed-loop system trajectories under an online learning-based control law. We employ a sampling-based approximation and exploit system properties to prove that the computed confidence regions are correct with high probability. In a numerical simulation, we show that the proposed approach accurately predicts correct confidence regions.

Keywords: Machine learning, Multi-agent systems, Randomized methods
Abstract: The Guaranteed Error Machine (GEM) is a classification algorithm that allows the user to set a-priori (i.e., before data are observed) an upper bound on the probability of error. Due to its strong statistical guarantees, GEM is of particular interest for safety critical applications in control engineering. Empirical studies have suggested that a pool of GEM classifiers can be combined in a majority voting scheme to boost the individual performances. In this paper, we investigate the possibility of keeping the probability of error under control in the absence of extra validation or test sets. In particular, we consider situations where the classifiers in the pool may have different guarantees on the probability of error, for which we propose a data-dependent weighted majority voting scheme. The preliminary results presented in this paper are very general and apply in principle to any weighted majority voting scheme involving individual classifiers that come with statistical guarantees, in the spirit of Probably Approximately Correct (PAC) learning.

Keywords: Dynamic Networks, Distributed control and estimation, Stochastic system identification
Abstract: The definitions of delayed mutual information and multi-information are recalled. It is shown how the delayed mutual information may be used to reconstruct the interaction topology resulting from some unknown scale-free graph with its associated local dynamics. Delayed mutual information is also used to solve the community detection problem. A probabilistic voter model defined on a scale-free graph is used throughout the paper as an illustrative example.

Keywords: Dynamic Networks, Estimation and filtering, Control and estimation with data loss
Abstract: This paper is concerned with the robust optimal estimation problem based on the prediction compensation mechanism for dynamical networks with time-varying parameters, where communication delays and degraded measurements are considered. The missing measurements are characterized by some random variables governed by Bernoulli distribution, where each sensor having individual missing probability is reflected. During the signal transmissions through the communication networks, the network-induced communication delays commonly exist among the adjacent nodes transmissions and a prediction updating method is given to compensate the caused impacts. Accordingly, a time-varying state estimator with hybrid compensation scheme is constructed such that, for both the communication delays and missing measurements, a minimized upper bound matrix with regards to the estimation error covariance matrix is found and an explicit estimator parameter matrix is designed at each sampling step accordingly. Finally, the comparative simulations are given to validate the advantages of main results.

Keywords: Dynamic Networks, Identification for control, Identifiability
Abstract: The interconnection of complex devices in network structures has been a challenging topic in the system identification research domain. This study presents the model identification of autonomous vehicles in platoon formation, which can be cast as a dynamic network. The paper presents the comparison between two network structures: (i) a vehicle-based network, which considers the interconnection between the vehicles based only on the velocity measurements, and (ii) a sensor-based network that considers the available sensor, i.e. the velocity and the relative distance measurements. The comparison is based on the difference between the identified transfer functions and the true ones, and the analysis of the identified air resistance coefficient variances. In addition, the paper presents the identifiability requirements for both network topologies. Simulation results show that for the same data set the variance of the identified parameters can be almost five times smaller if the system is represented as a sensor-based network, but some conditions to guarantee the identifiability of this network structure must be fulfilled.

Keywords: Dynamic Networks, Multi-agent systems, Consensus
Abstract: The desynchronization problems in oscillatory networks is considered. A new desynchronization notion is introduced and desynchronization conditions are provided. The desynchronization notion is formulated in terms of Yakubovich oscillatority of the auxiliary synchronization error system. As an example, the network of diffusively coupled FitzHugh-Nagumo systems with undirected graph is considered. The simple inequality guaranteeing network desynchronization is derived. The simulation results confirm the validity of the obtained analytical results.

Keywords: Identification for control, Multi-agent systems, Identifiability
Abstract: We propose a method to efficiently estimate the Laplacian eigenvalues of an arbitrary, unknown network of interacting dynamical agents. The inputs to our estimation algorithm are measurements about the evolution of a collection of agents (potentially one) during a finite time horizon; notably, we do not require knowledge of which agents are contributing to our measurements. We propose a scalable algorithm to exactly recover a subset of the Laplacian eigenvalues from these measurements. These eigenvalues correspond directly to those Laplacian modes that are observable from our measurements. We show how our technique can be applied to networks of multiagent systems with arbitrary dynamics in both continuous- and discrete-time. Finally, we illustrate our results with numerical simulations.

Keywords: Machine learning, Consensus and Reinforcement learning control, Multi-agent systems
Abstract: In contrast to its great empirical success, theoretical understanding of multi-agent reinforcement learning (MARL) remains largely underdeveloped. As an initial attempt, we provide a finite-sample analysis for decentralized cooperative MARL with networked agents. In particular, we consider a team of cooperative agents connected by a time-varying communication network, with no central controller coordinating them. The goal for each agent is to maximize the long-term return associated with the team-average reward, by communicating only with its neighbors over the network. A batch MARL algorithm is developed for this setting, which can be implemented in a decentralized fashion. We then quantify the estimation errors of the action-value functions obtained from our algorithm, establishing their dependence on the function class, the number of samples in each iteration, and the number of iterations. This work appears to be the first finite-sample analysis for decentralized cooperative MARL from batch data.

Keywords: Identifiability, Nonlinear system identification, Identification for control
Abstract: Observabililty is an important topic of Boolean control networks (BCNs). In this paper, we propose a new type of observability named online observability to present the sufficient and necessary condition of determining the initial states of BCNs, when their initial states cannot be reset. And we design an algorithm to decide whether a BCN has the online observability. Moreover, we prove that a BCN is identifiable iff it satisfies the controllability and the online observability, which reveals the essence of identification problem of BCNs.

Keywords: Grey box modelling, Identification for control, Nonlinear system identification
Abstract: Knowing where wastewater is flowing in sewer networks is essential to optimize system operation. Unfortunately, flow in gravity-driven sewers is subject to transport delays and typically disturbed by significant domestic, ground, and rain inflows. In this work, we utilize a lumped-parameter hydrodynamic model with a bi-linear structure for identifying these delays, decouple disturbances and to predict the discharged flow. We use pumped inlet and discharged dry-weather flow data to estimate the model parameters. Under mild assumptions on the domestic and groundwater inflows, i.e. disturbances, we show that decoupling these inflows from the total discharge is possible. A numerical case study on an EPA Storm Water Management Model and experimental results on a real network demonstrate the proposed method.

Keywords: Hybrid and distributed system identification
Abstract: The identification of switched systems involves solving a mixed-integer optimization problem to determine the parameters of each mode dynamics (continuous part) and assign the data samples to the modes (discrete part), so as to minimize a cost criterion measuring the quality of the model on a set of input/output data collected from the system. Oftentimes, some a priori information on the switching mechanism is available, e.g., in the form of a minimum dwell time. This information can be encoded in a suitable constraint and included in the optimization problem, but this introduces a coupling between the discrete and continuous optimization variables that makes the problem harder to solve. In this paper, we propose an iterative approach to the identification of switched systems that alternates a minimization step with respect to the continuous parameters of the modes, and a minimization step with respect to the discrete variables defining the sample-mode mapping. Constraints originating from prior knowledge on the switching mechanism are taken into account after the (unconstrained) discrete optimization step through a post-processing phase. These three phases are repeated until a stopping criterion is met. A comparative numerical analysis of the proposed method shows its improved performance with respect to competitive approaches in the literature.

Keywords: Hybrid and distributed system identification, Identification for control
Abstract: This paper introduces a novel methodology for the identification of switching dynamics for switched autoregressive linear models. Switching behavior is assumed to follow a Markov model. The system's outputs are contaminated by possibly large values of measurement noise. Although the procedure provided can handle other noise distributions, for simplicity, it is assumed that the distribution is Normal with unknown variance. Given noisy input-output data, we aim at identifying switched system coefficients, parameters of the noise distribution, dynamics of switching and probability transition matrix of Markovian model. System dynamics are estimated using previous results which exploit algebraic constraints that system trajectories have to satisfy. Switching dynamics are computed with solving a maximum likelihood estimation problem. The efficiency of proposed approach is shown with several academic examples. Although the noise to output ratio can be high, the method is shown to be effective in the situations where a large number of measurements is available.

Keywords: Hybrid and distributed system identification, Identification for control, Learning for control
Abstract: We propose a theoretical framework for joint system identification and control on a class of stochastic linear systems. We investigate optimization algorithms for inferring endogenous and environmental parameters from data, part of which are used for control purposes. A number of non-trivial interplays among stability and performance, as well as computational challenges and fundamental limits in identification rate emerge. Our results are validated via simulation example on a quadcopter control problem.

Keywords: Hybrid and distributed system identification, Nonlinear system identification, Identification for control
Abstract: This paper presents a systematic identification process for the hybrid dynamical system (HDS) estimating not only the coefficients but also the structure of the model. Generally speaking, the system identification is used for the HDS system that the model structure, the number of modes, and the explanatory variables of the model are unknown. In the proposed method, a quantitative index to evaluate the number of modes is deployed and the optimal number of modes is determined from the measurement. Model selection method is also introduced to determine the explanatory variables in each mode in a systematic manner. Two of piece-wise linear models which are well known as the HDS models are used for the targeting system to identify, and the validity of the proposed method is demonstrated. Finally, the result of system identification in comparison with the conventional system identification method for HDS is discussed.

Keywords: Hybrid and distributed system identification, Nonlinear system identification, Recursive identification
Abstract: The paper presents an algorithm for the identification of PieceWise Affine Output-Error (PWA-OE) models, which involves the estimation of the parameters defining affine submodels as well as a partition of the regressor space. For the estimation of affine submodel parameters, a bias-correction scheme is presented to correct the bias in the least squares estimates which is caused by the output-error noise structure. The obtained bias-corrected estimates are proven to be consistent under suitable assumptions. The bias-correction method is then combined with a recursive estimation algorithm for clustering the regressors. These clusters are used to compute a partition of the regressor space by employing linear multi-category discrimination. The effectiveness of the proposed methodology is demonstrated via a simulation case study.

Keywords: Identifiability, Nonlinear system identification
Abstract: To obtain a consistent estimate when performing an identification with Prediction Error, it is important that the excitation yields informative data with respect to the chosen model structure. While the characterization of this property seems to be a mature research area in the linear case, the same cannot be said for nonlinear systems. In this work, we study the data informativity for a particular type of Hammerstein systems for two commonly-used excitations: white Gaussian noise and multisine. The real life example of the MEMS gyroscope is considered.

Keywords: Identification for control, Machine learning, Nonlinear system identification
Abstract: The prediction uncertainty of a neural network is considered from a classical system identification point of view. To know this uncertainty is extremely important when using a network in decision and feedback applications. The asymptotic covariance of the internal parameters in the network due to noise in the observed dependent variables (output) and model class mismatch, i.e., the true system cannot be exactly described by the model class, is first surveyed. This is then applied to the prediction step of the network to get a closed form expression for the asymptotic, in training data information, prediction variance. Another interpretation of this expression is as the non-asymptotic Cramér-Rao Lower Bound. To approximate this expression, only the gradients and residuals, already computed in the gradient descent algorithms commonly used to train neural networks, are needed. Using a toy example, it is illustrated how the uncertainty in the output of a neural network can be estimated.

Keywords: Identifiability, Nonlinear system identification, Identification for control
Abstract: This paper introduces the profile likelihood method in order to assess simultaneously the parameter identifiability and the state observability for nonlinear dynamic state-space models with constant parameters. While a formal definition of a parameter’s identifiability has been used before, the novel idea is to investigate also the state’s observability by the identifiability of its initial value. Using the profile likelihood, both qualitative as well as quantitative statements are drawn from the analysis based on the nonlinear model and (possibly noisy) sensor data. A simplified wind turbine model is presented and used as an application example for the profile likelihood approach in order to investigate the model’s usability for state and parameter estimation. It is shown that the critical model parameters and initial states are identifiable in principle. The analysis with more complex models and realistic data reveals the limitations when assumptions are deliberately violated in order to meet reality.

Keywords: Nonlinear system identification, Bounded error identification, Particle filtering/Monte Carlo methods
Abstract: The development of Particle Filters has made possible state estimation of dynamic systems presenting non-linear dynamics and potential multi-modalities. However, the efficiency of these approaches depends tightly of the required number of particles which may prove very high to approximate large range of uncertainty on the process or the measurements. To overcome this issue, the Box-Particle Filter (BPF) combines the versatility of the Particle Filter and the robustness of set-membership algorithms. The particles are replaced by boxes which represent in a compact way large variations of the estimates. Although this filter presents various advantages and requires a small number of boxes to estimate the state, the resulting estimates may prove pessimistic, as the uncertainty description as unions of axis-aligned intervals can be rather rough and doesn't account for potential dependencies between the resulting estimate components. In the proposed paper, a new version of the BPF is proposed. Boxes are replaced by polytopes (multidimensional polygons) in the filter algorithm, so that they can adapt to represent state components dependency. This modification tends to ameliorate the estimation precision (i.e. the size of the final set that includes the true state decreases) while keeping the number of required polyhedrons small. Several examples illustrate the benefits of such an approach.

Keywords: Nonlinear system identification, Closed loop identification, Nonparametric methods
Abstract: In this paper, we propose a non-parametric state-space identification approach for open-loop and closed-loop discrete-time nonlinear systems with multiple inputs and multiple outputs. Employing a least squares support vector machine (LS-SVM) approach in a reproducing kernel Hilbert space framework, a nonlinear auto-regressive model with exogenous terms is identified to provide a non-parametric estimate of the innovation noise sequence. Subsequently, this estimate is used to obtain a compatible non-parametric estimate of the state sequence in an unknown basis using kernel canonical correlation analysis. Finally, the estimate of the state sequence is used together with the estimated innovation noise sequence to find a non-parametric state-space model, again using a LS-SVM approach. The performance of the approach is analyzed in a simulation study with a nonlinear system operating both in open loop and closed loop. The identification approach can be viewed as a nonlinear counterpart of consistent subspace identification techniques for linear time-invariant systems operating in closed loop.

Keywords: Nonlinear system identification, Grey box modelling
Abstract: This work deals with a class of nonlinear regression models called second-order modulus models. It is shown that the possibility of obtaining consistent parameter estimators for these models depends on how process disturbances enter the system. Two scenarios where consistency can be achieved for instrumental variable estimators despite non-additive system disturbances are demonstrated, both in theory and by simulation examples.

Keywords: Nonlinear system identification, Hybrid and distributed system identification
Abstract: This paper considers the problem of identifying the linear portion of a Wiener system, for the case of a known, but non-invertible output non-linearity. It is well known that this scenario, common in many practical applications, leads to problems that are generically NP-hard in the number of experiments. Thus, existing techniques scale poorly and are typically limited to relatively few points. The main result of this paper shows that this difficulty can be circumvented by considering an algebraic motivated approach. Specifically, we show that the problem is equivalent to identification of a switched linear system generated from the observed data. In turn, this problem can be solved by recasting it as the problem of finding the vanishing ideal of an arrangement of subspaces, a task that reduces to finding the null space of an embedded data matrix constructed from the observed data.

Keywords: Nonlinear system identification, Identification for control
Abstract: In this paper, we propose a novel approach for the identification from data of an unknown nonlinear function together with its derivatives. This approach can be useful, for instance, in the context of nonlinear system identification for obtaining models that are more reliable than the traditional ones, based on plain function approximation. Indeed, models identified by accounting for the derivatives can provide a better performance in several tasks, such as multi-step prediction, simulation, and control design. We also develop an optimality analysis, showing that models derived using this approach enjoy suitable optimality properties in Sobolev spaces. We finally demonstrate the effectiveness of the approach with a numerical example.

Keywords: Nonlinear system identification, Identification for control, Continuous time system estimation
Abstract: In this paper, we develop the Koopman operator theory for dynamical systems with symmetry. In particular, we investigate how the Koopman operator and eigenfunctions behave under the action of the symmetry group of the underlying dynamical system. Further, exploring the underlying symmetry, we propose an algorithm to construct a global Koopman operator from local Koopman operators. In particular, we show, by exploiting the symmetry, data from all the invariant sets are not required for constructing the global Koopman operator; that is, local knowledge of the system is enough to infer the global dynamics.

Keywords: Nonlinear system identification, Identification for control, Machine learning
Abstract: In recent years, the Koopman operator was the topic of many extensive investigations in the nonlinear system identification community. Especially, when dealing with nonlinear systems no straight forward method is available to identify systems of this class. In modern data science a standard method is using artificial neural networks to extract models from data. This method is mainly used when there is a certain function behind the measured data, but little other information is available. This paper combines the Koopman framework and artificial neural networks to achieve a linear model for nonlinear systems. The structure of the network is similar to an autoencoder. The input part is the encoder which itself consists of two different parts. The first part propagates the measurements directly to the middle part. The second encoder introduces the state-space lifting which characterizes the Koopman framework. The middle layer of the network represents an estimation of a linear state-space system that acts on a Koopman operator invariant subspace. After this layer, the extended state-space must be decoded so that the outputs of the Koopman linear system are functions of the true states. The method is evaluated with a single pendulum and a nonlinear yeast glycolysis model. Additionally, we show the advantage of considering inputs as true inputs rather than additional states.

Keywords: Nonlinear system identification, Machine learning, Grey box modelling
Abstract: This paper investigates the local linear model tree (LOLIMOT) with optimized structure. The performance of the LOLIMOT model depends on how the neurons are constructed. In the typical LOLIMOT model, the number of neurons is initially set as one and starts to increase by repeatedly splitting an existing neuron into two equal ones until the required performance is achieved. Because the equal split of a neuron is not optimal, a large model size is often necessary for required performance, leading to high complexity and strong overfitting. In this paper, we propose a gradient-decent-search-based algorithm to optimally split an existing neuron into two new ones. Based on both numerical data and simulated engine data, through the evaluation of optimized structure, the effectiveness of proposed method has been verified.

Keywords: Nonlinear system identification, Machine learning, Identification for control
Abstract: This paper addresses a learning problem for nonlinear dynamical systems with incorporating any specified dissipativity property. The nonlinear systems are described by the Koopman operator, which is a linear operator defined on the infinite-dimensional lifted state space. The problem of learning the Koopman operator under specified quadratic dissipativity constraints is formulated and addressed. The learning problem is in a class of the non-convex optimization problem due to nonlinear constraints and is numerically intractable. By applying the change of variable technique and the convex overbounding approximation, the problem is reduced to sequential convex optimization and is solved in a numerically efficient manner. Finally, a numerical simulation is given, where high modeling accuracy achieved by the proposed approach including the specified dissipativity is demonstrated.