Max-plus-linear model-based predictive control for constrained hybrid systems: linear programming solution

In this paper, a linear programming method is proposed to solvemodel predictive control for a class of hybrid systems. Firstly,using the (max, +) algebra, a typical subclass of hybrid systemscalled max-plus-linear (MPL) systems is obtained. And then, modelpredictive control (MPC) framework is extended to MPL systems. Ingeneral, the nonlinear optimization approach or extended linearcomplementarity problem (ELCP) were applied to solve the MPL-MPCoptimization problem. A new optimization method based on canonicalforms for max-min-plus-scaling (MMPS) functions (using theoperations maximization, minimization, addition and scalarmultiplication) with linear constraints on the inputs is presented.The proposed approach consists in solving several linear programmingproblems and is more efficient than nonlinear optimization. Thevalidity of the algorithm is illustrated by an example.