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.

学习方法与模型预测控制 (MPC) 的结合在最近的文献中引起了大量关注。这种组合的希望是减少 MPC 方案对精确模型的依赖，并利用快速发展的机器学习和强化学习工具来利用可用于许多系统的不断增长的数据量。特别是，强化学习和 MPC 的结合已被提议作为一种可行且理论上合理的方法，用于在强化学习中引入可解释、安全和稳定的策略。但是，仍然缺乏详细说明如何通过学习工具提供的参数更新来维持基于 MPC 的策略的安全性和稳定性的正式理论。本文解决了这一差距。该理论是针对通用稳健 MPC 案例开发的，并应用于基于管的稳健线性 MPC 案例的仿真，该理论在实践中相当容易部署。该论文侧重于将强化学习作为一种学习工具，但它适用于任何在线更新 MPC 参数的学习方法。