Model predictive control for max-plus-linear discrete event systems

摘要

Model predictive control (MPG) is a very popular controller design method in the process industry. A key advantage of MPG is that it can accommodate constraints on the inputs and outputs. Usually MPG uses linear discrete-time models. In this paper we extend MPG 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.