Robust Model Predictive Control Based on Stabilizing Parameter Space Calculus

The aim of this study is to introduce a novel approach for robust model predictive control (MPC) design based on stabilizing parameter spaces. In order to determine the stabilizing parameter regions, a Lyapunov equation based approach is proposed for nominal systems. In addition to the free controller parameters, it is also possible to determine boundaries of uncertain parameters in the present approach. The precomputed stability conditions on controller parameters are inserted to the MPC problem formulation as constraints. By this way, the stability of the closed-loop system is ensured. The proposed approach allows to design the nominal MPC, instead of the robust one. Using the predetermined constraints, the MPC is implemented to optimize the controller parameters over this stabilizing set. This paper introduces three particular control scenarios that tune the basic properties of the novel approach, e.g., runtime and computational effort. Two illustrative case studies are presented to demonstrate the efficiency of the proposed robust MPC strategy.