T.J.J. van den Boom and B. De Schutter, "MPC for max-plus-linear systems with an output cost criterion: Steady-state behavior and guaranteed stability," Proceedings of the Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, Shanghai, China, pp. 2286-2291, Dec. 2009.
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 steady-state behavior of these so-called max-plus-linear systems in the case of an output cost criterion. We derive improved tuning rules for the controller parameters that guarantee us a feasible and stable operation of the controller in the unconstrained case. An example shows that violation of the tuning rules may destabilize the closed-loop system.