Theory-orientated: Development of Set-based Methods for Parameter Estimation Considering Uncertainties

Mathematical modeling and analysis of non-linear, dynamic systems and model-based predictions play an important role, e.g. in systems biology and control engineering. Often experimental data for model validation are of qualitative as well as quantitative nature and hard to combine. Furthermore, model parameters, data and structure are erroneous due to limited knowledge. Recently, set-based methods have been developed to estimate consistent sets of parameters. Thereby, all uncertainties of the system are considered and formulated in a feasibility problem. This feasibility problem can be solved efficiently by convex relaxation and optimization [1,2].
Lately, a method which introduces binary variables to represent logical relations in models was developed in our group [3]. This allows to combine qualitative statements such as "if x is present, then formation of y is reduced" with quantitative models.

Within the framework of a Bachelor/Master/Student/Diploma-thesis project, students may work on several topics and questions including (but not limited to):

• development of new methods for set-based parameter estimation and identification, e.g. extension of [3]
• implementation of the methods in a Matlab-based toolbox for systems analysis and demonstration by means of selected and relevant examples, e.g. from systems biology [4,5]

For a successful project, the student should have

• strong interest in theoretical work
• good knowledge of systems and control theory
• good knowledge of MatLab.

Always possible

For further information or to apply, please contact Nadine Rudolph (nadine.rudolph@ovgu.de).

• [1] Rudolph, N., Meyer, T., Franzen, K., Garbers, C., Streif, S., Schaper, F., Dittrich, A. and Findeisen, R., A Two-level Approach for Fusing Early Signaling Events and Long Term Biological Responses. In International Symposium on Advanced Control of Chemical Processes (ADCHEM), pages 1229-1234, Whistler, Canada, June 2015.
• [2] Streif, S., Strobel, N. and Findeisen, R., Inner Approximations of Consistent Parameter Sets Via Constraint Inversion and Mixed-integer Linear Programming. In Proc. of the 12th IFAC Symposium on Computer Applications in Biotechnology (CAB), pages 326-331, Mumbai, India, December 2013.
• [3] Rumschinski, P., Borchers, S., Bosio, S., Weismantel, R. & Findeisen, R., Set-based dynamical parameter estimation and model invalidation for biochemical reaction networks.BMC Syst Biol, 2010, Vol. 4, pp. 69
• [4] Rumschinski, P., Borchers, S., Bosio, S., Weismantel, R. & Findeisen, R., Set-based dynamical parameter estimation and model invalidation for biochemical reaction networks.BMC Syst Biol, 2010, Vol. 4, pp. 69
• [5] Henrion, D. and Lasserre, J.-B., Detecting global optimality and extracting solutions in GloptiPoly. Lecture Notes on Control and Information Sciences, 2005, Vol. 312, Springer Verlag, Berlin
• [6] Rumschinski, P., Streif, S., Findeisen, R., Combining qualitative information and semi-quantitative data for guaranteed invalidation of biochemical network models. International Journal of Robust and Nonlinear Control, 2012, Vol. 22, pp. 1157-1173
• [7] Streif, S., Savchenko, A., Rumschinski, P., Borchers, S. and Findeisen, R., ADMIT: a toolbox for guaranteed model invalidation, estimation and qualitative-quantitative modeling. Bioinformatics, 2012, 28(9):1290-1291. [5] Palsson, B. O. and Lightfoot, E. N. Mathematical modeling of dynamics and control in metabolic networks. I. On Michaelis-Menten kinetics, Journal of Theoretical Biology, 1984, Vol. 111, pp. 273 – 302
• [8] Palsson, B. O. and Lightfoot, E. N., Mathematical modeling of dynamics and control in metabolic networks. I. On Michaelis-Menten kinetics, Journal of Theoretical Biology, 1984, Vol. 111, pp. 273 – 302

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