Robust Model Predictive Control for Constrained Uncertain Systems Based on Concentric Container and Varying Tube

Abstract

This paper proposes a novel robust model predictive control (RMPC) method for the stabilization of constrained systems subject to additive disturbance (AD) and multiplicative disturbance (MD). Concentric containers are introduced to facilitate the characterization of MD, and varying tubes are constructed to bound reachable states. By restricting states and the corresponding inputs in containers with free sizes and a fixed shape, feasible MDs, which are the products of model uncertainty with states and inputs, are restricted into polytopes with free sizes. Then, tubes with different centers and shapes are constructed based on the nominal dynamics and the knowledge of AD and MD. The free sizes of containers allow for a more accurate characterization of MD, while the fixed shape reduces online computational burden, making the proposed method less conservative and computationally efficient. Moreover, the shape of containers is optimized to further reduce conservativeness. Compared to the RMPC method using homothetic tubes, the proposed method has a larger region of attraction while involving fewer decision variables and constraints in the online optimization problem.