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Min-Max Model Predictive Control for Uncertain Max-Min-Plus-Scaling Systems

We extend the model predictive control (MPC) framework that has been developed previously to a class of uncertain discrete event systems that can be modeled using the operations maximization, minimization, addition and scalar multiplication. This class encompasses max-plus-linear systems, min-max-plus systems, bilinear max-plus systems and polynomial max-plus systems. We first consider open-loop min-max MPC and we show that the resulting optimization problem can be transformed into a set of linear programming problems. Then, min-max feedback model predictive control using disturbance feedback policies is presented, which leads to improved performance compared to the open-loop approach