  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.
