B. De Schutter and T. van den Boom, "Model predictive control for max-plus-linear systems," Proceedings of the 2000 American Control Conference, Chicago, Illinois, pp. 4046-4050, June 2000.
Model predictive control (MPC) is a very popular controller design method in the process industry. An important advantage of MPC is that it allows the inclusion of constraints on the inputs and outputs. Usually MPC uses linear discrete-time models. In this paper we extend MPC to a class of discrete event systems, i.e. we present an MPC framework for max-plus-linear systems. In general the resulting optimization problem is nonlinear and nonconvex. However, if the control objective and the constraints depend monotonically on the outputs of the system, the MPC problem can be recast as problem with a convex feasible set. If in addition the objective function is convex, this leads to a convex optimization problem, which can be solved very efficiently.