T.J.J. van den Boom and B. De Schutter, "MPC for max-plus-linear systems with guaranteed stability," Proceedings of the 16th IFAC World Congress, Prague, Czech Republic, pp. 1-6, July 2005.
Model predictive control (MPC) is a popular controller design technique in the process industry. Conventional MPC uses linear or nonlinear discrete-time models. Previously, we have extended MPC to a class of discrete event systems that can be described by a model that 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 function can be seen as a Lyapunov function for the system and can thus be used to prove stability.