Model predictive control for max-min-plus systems

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. Introduction Conventional control design techniques such as pole placement, LQG, H∞, H2, . . . yield optimal controllers or control input sequences for the entire future evolution of the system. Extending these methods to include additional constraints on the inputs and outputs is not easy. However, Model Predictive Control (MPC) easily allows the inclusion of such constraints due to the use of a receding finite horizon strategy. This advantage, in combination with the low computational requirements and the possibility to deal with slowly time-varying systems, has led to a widespread use of MPC in the process industry. Traditionally MPC uses