Safe Reinforcement Learning with Stability & Safety Guarantees Using Robust MPC

Reinforcement Learning offers tools to optimize policies based on the data obtained from the real system subject to the policy. While the potential of Reinforcement Learning is well understood, many critical aspects still need to be tackled. One crucial aspect is the issue of safety and stability. Recent publications suggest the use of Nonlinear Model Predictive Control techniques in combination with Reinforcement Learning as a viable and theoretically justified approach to tackle these problems. In particular, it has been suggested that robust MPC allows for making formal stability and safety claims in the context of Reinforcement Learning. However, a formal theory detailing how safety and stability can be enforced through the parameter updates delivered by the Reinforcement Learning tools is still lacking. This paper addresses this gap. The theory is developed for the generic robust MPC case, and further detailed in the robust tube-based linear MPC case, where the theory is fairly easy to deploy in practice.