I. Necoara, B. De Schutter, T. van den Boom, and H. Hellendoorn, "Min-max model predictive control for uncertain max-min-plus-scaling systems," Proceedings of the 8th International Workshop on Discrete Event Systems (WODES'06), Ann Arbor, Michigan, pp. 439-444, July 2006.
We extend the model predictive control (MPC) framework that has been developed previously to a class of uncertain discrete event systems that can be modeled using the operations maximization, minimization, addition and scalar multiplication. This class encompasses max-plus-linear systems, min-max-plus systems, bilinear max-plus systems and polynomial max-plus systems. We first consider open-loop min-max MPC and we show that the resulting optimization problem can be transformed into a set of linear programming problems. Then, min-max feedback model predictive control using disturbance feedback policies is presented, which leads to improved performance compared to the open-loop approach.