I. Necoara, B. De Schutter, T. van den Boom, and H. Hellendoorn, "Model predictive control for uncertain max-min-plus-scaling systems," International Journal of Control, vol. 81, no. 5, pp. 701-713, May 2008.
In this paper we extend the classical min-max model predictive control framework to a class of uncertain discrete event systems that can be modeled using the operations maximization, minimization, addition and scalar multiplication, and that we call max-min-plus-scaling (MMPS) systems. Provided that the stage cost is an MMPS expression and considering only linear input constraints then the open-loop min-max model predictive control problem for MMPS systems can be transformed into a sequence of linear programming problems. Hence, the min-max model predictive control problem for MMPS systems can be solved efficiently, despite the fact that the system is nonlinear. A min-max feedback model predictive control approach using disturbance feedback policies is also presented, which leads to improved performance compared to the open-loop approach.