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Robust Explicit/Multi—parametric Model Predictive Control for Box-Constrained Linear Dynamic Systems

Abstract Robust explicit/multi-parametric controllers are designed for constrained, linear discrete–time systems with box-constrained states and inputs, involving uncertainty in the left–hand side (LHS) of the Model Predictive Control (MPC) optimization model. Based on previous results, this work presents a new algorithm that features: (i) a dynamic programming reformulation of the MPC optimization, (ii) a robust reformulation of the constraints that accounts for uncertainty and (iii) a multi–parametric programming solution step where the controls are obtained as an explicit function of the states.