An Approximation Approach for Model Predictive Control of Stochastic Max-Plus Linear Systems

Model Predictive Control (MPC) is a model-based control method based on a receding horizon approach and online optimization. In previous work we have extended MPC to a class of discrete-event systems, namely the max-plus linear systems, i.e., models that are “lineal” in the max-plus algebra. Lately, the application of MPC for stochastic max-plus-linear systems has attracted a lot of attention. At each event step, an optimization problem then has to be solved that is, in general, a highly complex and computationally hard problem. Therefore, the focus of this paper is on decreasing the computational complexity of the optimization problem. To this end, we use an approximation approach that is based on the p-th raw moments of a random variable. This method results in a much lower computational complexity and computation time while still guaranteeing a good performance.