B. De Schutter and T. van den Boom, "Model predictive control for max-min-plus systems," in Discrete Event Systems: Analysis and Control (Proceedings of the 5th International Workshop on Discrete Event Systems (WODES2000), Ghent, Belgium, Aug. 2000) (R. Boel and G. Stremersch, eds.), vol. 569 of The Kluwer International Series in Engineering and Computer Science, Boston, Massachusetts: Kluwer Academic Publishers, ISBN 0-7923-7897-0, pp. 201-208, 2000.
Model predictive control (MPC) is a widely used control design method in the process industry. Its main advantage is that it allows the inclusion of constraints on the inputs and outputs. Usually MPC uses linear discrete-time models. We extend MPC to max-min-plus discrete event systems. In general the resulting optimization problems are nonlinear and nonconvex. However, if the state equations are decoupled and if the control objective and the constraints depend monotonically on the states and outputs of system, the max-min-plus-algebraic 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.