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

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 refines the parameter estimates online 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 a robust adaptive MPC scheme without iterative learning of the terminal ingredients.