Model predictive control for perturbed max-plus-linear systems: a stochastic approach

Model predictive control (MPC) is a popular controller design technique in the process industry. Conventional MPC uses linear or nonlinear discrete-time models. Previously, we (2001) have extended MPC to a class of discrete event systems that can be described by a model that is "linear" in the (max, +) algebra. In our previous work we have only considered MPC for the perturbations-free case and for the case with bounded noise and/or modeling errors. We extend our previous results on MPC for perturbed max-plus-linear systems to a stochastic setting. We show that under quite general conditions the resulting optimization problems turn out to be convex and can be solved very efficiently