Model predictive control for uncertain max–min-plus-scaling systems

Abstract

In this paper we extend the classical min–max model predictive control framework to a class of uncertain discrete event systems that can be modelled using the operations maximization, minimization, addition and scalar multiplication, and that we call max–min-plus-scaling (MMPS) systems. Provided that the stage cost is an MMPS expression and considering only linear input constraints then the open-loop min–max model predictive control problem for MMPS systems can be transformed into a sequence of linear programming problems. Hence, the min–max model predictive control problem for MMPS systems can be solved efficiently, despite the fact that the system is non-linear. A min–max feedback model predictive control approach using disturbance feedback policies is also presented, which leads to improved performance compared to the open-loop approach.

Acknowledgments

Research supported by the STW projects “Model predictive control for hybrid systems” (DMR. 5675), and “Multiagent control of large-scale hybrid systems” (DWV. 6188), and by the European IST project “Modelling, Simulation and Control of Non-smooth Dynamical Systems (SICONOS)” (IST-2001-37172) and by the European 6th Framework Network of Excellence “HYbrid CONtrol: Taming Heterogeneity and Complexity of Networked Embedded Systems (HYCON)”.