MPC for max-plus-linear systems with guaranteed stability

Authors:	van den Boom Ton J.J., Delft University of Technology, Netherlands De Schutter B., Delft University of Technology, Netherlands
Topic:	1.3 Discrete Event and Hybrid Systems
Session:	Analysis and Control of Discrete Event Systems
Keywords:	discrete event systems, model predictive control, max-plus-linear systems, Lyapunov stability

Abstract

Model predictive control (MPC) is a popular controller designtechnique in the process industry. Conventional MPC uses linear ornonlinear discrete-time models. Previously, we have extended MPC to aclass of discrete event systems that can be described by a modelthat is `linear' in the max-plus algebra.In this paper we consider the stability of MPC for these max-plus linear (MPL)systems, and we derive an MPL-MPC equivalent of the conventional end-point constraint.We show that with this end-point constraint the optimized cost functioncan be seen as a Lyapunov function for the system and can thus be used to prove stability.