OPTEC - K.U.Leuven Center of Excellence: Optimization in Engineering

"Robust control of a class of uncertain discrete event systems"
 
Ion Necoara (Delft University of Technology)

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.