Safe model-based Reinforcement Learning via Model Predictive Control and Control Barrier Functions

Optimal control strategies are often combined with safety certificates to ensure both performance and safety in safety-critical systems. A prominent example is combining Model Predictive Control (MPC) with Control Barrier Functions (CBF). Yet, efficient tuning of MPC parameters and choosing an appropriate class $\mathcal{K}$ function in the CBF is challenging and problem dependent. This paper introduces a safe model-based Reinforcement Learning (RL) framework where a parametric MPC controller incorporates a CBF constraint with a parameterized class $\mathcal{K}$ function and serves as a function approximator to learn improved safe control policies from data. Three variations of the framework are introduced, distinguished by the way the optimization problem is formulated and the class $\mathcal{K}$ function is parameterized, including neural architectures. Numerical experiments on a discrete double-integrator with static and dynamic obstacles demonstrate that the proposed methods improve performance while ensuring safety.