B. De Schutter and T.J.J. van den Boom, "Model predictive control for max-min-plus-scaling systems," Proceedings of the 2001 American Control Conference, Arlington, Virginia, pp. 319-324, June 2001.
We further extend the model predictive control framework, which is very popular in the process industry due to its ability to handle constraints on inputs and outputs, to a class of 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. In general the model predictive control problem for max-min-plus-scaling systems leads to a nonlinear non-convex optimization problem, that can also be reformulated as an optimization problem over the solution set of an extended linear complementarity problem. We also show that under certain conditions the optimization problem reduces to a convex programming problem, which can be solved very efficiently.