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

Reference:
B. De Schutter and T. van den Boom, "On model predictive control for max-min-plus-scaling discrete event systems," Tech. rep. bds:00-04, Control Systems Engineering, Fac. of Information Technology and Systems, Delft University of Technology, Delft, The Netherlands, 19 pp., June 2000.

Abstract:
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 max-plus-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.