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Robust control of a class of uncertain discrete event systems

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Abstract:
Discrete event systems are dynamical systems whose evolution equations changes in time by the occurrence of events. Discrete event systems that model only synchronization aspects are called max-plus-linear (MPL) systems. MPL systems can be described by models that are `linear' in the max-plus algebra. In this presentation we derive solutions to three types of finite-horizon min-max control problems for uncertain MPL systems, depending on the nature of the control input over which we optimize: open-loop input sequences, disturbances feedback policies, and state feedback policies. We assume that the uncertainty lies in a polytope, and that the closed-loop input and state sequence should satisfy a given set of linear inequality constraints for all admissible disturbance realizations. Despite the fact that the controlled system is nonlinear, we provide sufficient conditions that allow to preserve convexity of the optimal value function and its domain. As a consequence, by employing recent results in polyhedral algebra and multi-parametric linear programming we prove that the min-max control problems can be either recast as a linear program or solved via N multi-parametric linear programs, where N is the prediction horizon. In some particular cases of the uncertainty description (e.g. interval matrices), using results from dynamic programming, we show that the min-max control problem can be recast as a deterministic optimal control problem.

Type of Seminar:
Public Seminar
Speaker:
Dr.Ion Necoara
Delft Center for Systems and Control, Delft University of Technology , NL
Date/Time:
Nov 22, 2006   11:15
Location:

ETH Zentrum, Physikstrasse 3, Building ETL, Room K25
Contact Person:

Prof. John Lygeros
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Biographical Sketch:
Ion Necoara was born in Vrancea, Romania, on September 20, 1977. He received the B.Sc. degree in mathematics from the University of Bucharest, Faculty of Mathematics, and the M.Sc. degree in optimization and statistics from the same faculty in 2000 and 2002, respectively. After graduating he has been working as a Ph.D. student at the Delft Center for Systems and Control, Delft University of Technology, The Netherlands. In October this year he defended his thesis `Model predictive control for piecewise affine and max-plus-linear systems'. In 2005 he visited for 3 months the Control Group of Prof. Dr. J.Maciejowski, University of Cambridge, UK, where he worked together with Dr. E.Kerrigan on robust control for max-plus-linear systems. Ion Necoara is a member of the Dutch Institute of Systems and Control. His research interests are optimization in control, robust control, stability theory, large scale systems and hybrid systems.