  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.
