T. van den Boom and B. De Schutter, "Model predictive control for switching max-plus-linear systems with random and deterministic switching," Proceedings of the 17th IFAC World Congress, Seoul, Korea, pp. 7660-7665, July 2008.
Switching max-plus-linear (SMPL) systems are discrete event systems that can switch between different modes of operation. In each mode the system is described by a max-plus-linear state equation and a max-plus-linear output equation, with different system matrices for each mode. The switching may depend on input and state, or it may be a stochastic process. We derive a stabilizing model predictive controller for SMPL systems with both deterministic and stochastic switching. In general, the optimization in the MPC algorithm boils down to a nonlinear optimization problem, where the cost criterion is piecewise polynomial on polyhedral sets and the inequality constraints are linear.