On model predictive control for max-min-plus-scaling discrete event systems

We 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, and that we call max-min-plus-scaling systems. We show that this class encompasses several other classes of discrete event systems such as maxplus-linear systems, bilinear max-plus systems, polynomial max-plus systems, separated max-min-plus systems and regular max-min-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 solved using extended linear complementarity problems. We show that under certain conditions the optimization problem reduces to a convex programming problem, which can be solved very efficiently.