Differentiable Safe Controller Design through Control Barrier Functions

Learning-based controllers, such as neural network (NN) controllers, can show high empirical performance but lack formal safety guarantees. To address this issue, control barrier functions (CBFs) have been applied as a safety filter to monitor and modify the outputs of learning-based controllers in order to guarantee the safety of the closed-loop system. However, such modification can be myopic with unpredictable long-term effects. In this work, we propose a safe-by-construction NN controller which employs differentiable CBF-based safety layers, and investigate the performance of safe-by-construction NN controllers in learning-based control. Specifically, two formulations of controllers are compared: one is projection-based and the other relies on our proposed set-theoretic parameterization. Both methods demonstrate improved closed-loop performance over using CBF as a separate safety filter in numerical experiments.