The talk discusses the utilization of the set theoretic analysis in control synthesis and analysis under constraints and uncertainty. A methodology employing set dynamics and utilizing classical ideas from dynamical systems theory is invoked in order to discuss the minimality and the maximality of invariant sets as well as some computationally tractable control synthesis methods. Theoretical aspects concerned with the minimality and the maximality of invariant sets utilize fixed points of adequate image and preimage mappings induced from the underlying system dynamics, constraints on system variables and the uncertainty. It is revealed that the minimal and the maximal invariant sets are solutions, with special properties under, adequate but natural assumptions, of particular fixed point set equations. Properties of proposed fixed point set equations are also utilized to indicate the fragility of receding horizon control synthesis process with respect to arbitrarily small and feasible perturbations of ingredients of the underlying finite horizon optimal control problem. The power of the set dynamics approach is also invoked to re-examine briefly the minimality of invariant sets for linear discrete time systems and to devise a computationally tractable method for the calculation of the outer invariant approximations of the minimal invariant set. The set dynamics approach is also utilized to discuss, at the conceptual level, a simple tube receding horizon control synthesis method for a class of non-linear discrete time systems guaranteeing a-priori, under mild assumptions, strong system theoretic properties of the controlled, uncertain, dynamics.
Sasa V. Rakovic obtained the PhD degree in Control Theory from Imperial College London. His PhD thesis, entitled "Robust Control of Constrained Discrete Time Systems: Characterization and Implementation", was awarded the Eryl Cadwaladr Davies Prize as the best PhD thesis in the Electrical and Electronic Engineering Department of Imperial College London in 2005. He held posts of a Research Associate at Imperial College London (2004-11/2006) and a Postdoctoral Researcher at the ETH Zurich (11/2006-11/2008). He is currently a Scientific Associate at the Institute for Automation Engineering, Otto-von-Guericke-Universitat Magdeburg and an Honorary Research Associate at the CPSE of Imperial College London. His main research interests lie within the areas of control synthesis and analysis and decision making under constraints and uncertainty.