Approximate Optimal Control for Safety-Critical Systems with Control Barrier Functions

TL;DR

This paper introduces an approximate optimal control method using Control Barrier Functions that guarantees safety and convergence in safety-critical systems, overcoming limitations of traditional myopic approaches.

Contribution

The paper develops a novel approximate optimal control framework embedding safety violation costs into the value function, ensuring safety and convergence.

Findings

Guarantees safety and convergence to equilibrium.

Outperforms traditional quadratic programming in numerical tests.

Addresses infeasibility issues in safety-critical control.

Abstract

Control Barrier Functions (CBFs) have become a popular tool for enforcing set invariance in safety-critical control systems. While guaranteeing safety, most CBF approaches are myopic in the sense that they solve an optimization problem at each time step rather than over a long time horizon. This approach may allow a system to get too close to the unsafe set where the optimization problem can become infeasible. Some of these issues can be mitigated by introducing relaxation variables into the optimization problem; however, this compromises convergence to the desired equilibrium point. To address these challenges, we develop an approximate optimal approach to the safety-critical control problem in which the cost of violating safety constraints is directly embedded within the value function. We show that our method is capable of guaranteeing both safety and convergence to a desired equilibrium. Finally, we compare the performance of our method with that of the traditional quadratic programming approach through numerical examples.