Learning for MPC with stability & safety guarantees

The combination of learning methods with Model Predictive Control (MPC) has attracted a significant amount of attention in the recent literature. The hope of this combination is to reduce the reliance of MPC schemes on accurate models, and to tap into the fast developing machine learning and reinforcement learning tools to exploit the growing amount of data available for many systems. In particular, the combination of reinforcement learning and MPC has been proposed as a viable and theoretically justified approach to introduce explainable, safe and stable policies in reinforcement learning. However, a formal theory detailing how the safety and stability of an MPC-based policy can be maintained through the parameter updates delivered by the learning tools is still lacking. This paper addresses this gap. The theory is developed for the generic robust MPC case, and applied in simulation in the robust tube-based linear MPC case, where the theory is fairly easy to deploy in practice. The paper focuses on reinforcement learning as a learning tool, but it applies to any learning method that updates the MPC parameters online.