On MPC for max-plus-linear systems: Analytic solution and stability

In previous work we have extended the popular Model Predictive Control (MPC) design technique 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 study the analytic solution of the MPC controller for these max-plus- linear (MPL) systems and we compare this solution with other well-known control schemes. Furthermore, we derive tuning rules for the controller parameters that guarantee us a stable feasible and stable operation of the controller.