Robust learning in model predictive control

Abstract

This thesis presents a new robust adaptive learning Model Predictive Control (RALMPC) framework for linear and nonlinear systems subject to parametric uncertainties and additive disturbances, performing iterative tasks. The proposed approach integrates robust tube-based MPC with parameter adaptation and iterative learning. Parameter estimates are iteratively refined using set-membership estimation. Furthermore, by learning terminal ingredients-specifically, the terminal set and terminal cost-from data, the framework enhances closed-loop performance across iterations while ensuring robust safety guarantees. In particular, the method guarantees recursive feasibility, constraint satisfaction, and practical asymptotic stability of the closed-loop system. In the first part of the thesis, an RALMPC algorithm is developed for nonlinear systems, where the tube-based framework is constructed based on an incremental Lyapunov function. In the second part, the structure of linear systems is exploited to design a convex terminal set and cost, which results in a formulation with reduced computational complexity. For linear systems, instead of a general incremental Lyapunov function, the tube framework is based on polytopic sets to improve efficiency. The effectiveness of both formulations is demonstrated through numerical examples. The results show improved closed-loop performance and, in the linear case, a substantial reduction in computational burden compared to an existing robust adaptive MPC approach.