Risk-Aware Control: Integrating Worst-Case Conditional Value-At-Risk With Control Barrier Function

Abstract

In safety-critical control systems such as autonomous vehicles and medical devices, managing the risk of rare but severe tail events under uncertainty is crucial. This paper addresses this challenge by proposing a risk-aware control framework that integrates the worst-case conditional value-at-risk (CVaR) with control barrier functions (CBFs). Specifically, we formulate risk-aware safety constraints based on the worst-case CVaR, and show that the resulting risk-aware controllers can be computed via quadratic programs (for half-space and polytopic safe sets) or a semidefinite program (for ellipsoidal safe sets). Numerical simulations on an inverted pendulum illustrate that the proposed approach ensures safety under various scenarios and significantly reduces the safety constraint violation compared to existing CBF approaches. Overall, we show that incorporating worst-case CVaR into CBF design offers a tractable solution for safety-critical applications under uncertainty.