Model Predictive Control for Stochastic Switching Max-Plus-Linear Systems

A switching max-plus-linear system can operate in different modes. In each mode the system is described by a max-plus linear system equation. The switching may depend on the previous mode, on the state, and on the input. Stochastic switching max-plus-linear systems may include two types of stochastic uncertainty, namely stochastic parametric uncertainty and stochastic mode switching uncertainty. For both types of uncertainty results have appeared in the literature. In this paper we will consider stochastic switching max-plus-linear systems with parametric uncertainty and mode switching uncertainty in one single unified framework. First we derive a (general) model that includes both types of stochastic uncertainty. Next a model predictive control method is used to control the system, and we distinguish between the case where the two types of uncertainty are dependent or independent.