B. De Schutter and T. van den Boom, "Model predictive control for max-plus-linear discrete-event systems: Extended report & Addendum," Tech. rep. bds:99-10a, Control Systems Engineering, Fac. of Information Technology and Systems, Delft University of Technology, Delft, The Netherlands, 27 pp., Nov. 2000. A short version of this report has been published in 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 report 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 non-convex. 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.