B. De Schutter and T. van den Boom, "Model predictive control for max-plus-linear discrete event systems," Automatica, vol. 37, no. 7, pp. 1049-1056, July 2001.
Model predictive control (MPC) is a very popular controller design method in the process industry. A key advantage of MPC is that it can accommodate 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 that can be described by models that are "linear" in the max-plus algebra, which has maximization and addition as basic operations. In general the resulting optimization problem are nonlinear and nonconvex. However, if the control objective and the constraints depend monotonically on the outputs of the system, the model predictive control 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.