Robust MPC for Uncertain Linear Systems -- Combining Model Adaptation and Iterative Learning

Abstract: This paper presents a robust adaptive learning Model Predictive Control (MPC) framework for linear systems with parametric uncertainties and additive disturbances performing iterative tasks. The approach iteratively refines the parameter estimates using set membership estimation. Performance enhancement over iterations is achieved by learning the terminal cost from data. Safety is enforced using a terminal set, which is also learned iteratively. The proposed method guarantees recursive feasibility, constraint satisfaction, and a robust bound on the closed-loop cost. Numerical simulations on a mass-spring-damper system demonstrate improved computational efficiency and control performance compared to an existing robust adaptive MPC approach.