Risk-Aware Adaptive Control Barrier Functions for Safe Control of Nonlinear Systems under Stochastic Uncertainty

Abstract: This paper addresses the challenge of ensuring safety in stochastic control systems with high-relative-degree constraints, while maintaining feasibility and mitigating conservatism in risk evaluation. Control Barrier Functions (CBFs) provide an effective framework for enforcing safety constraints in nonlinear systems. However, existing methods struggle with feasibility issues and multi-step uncertainties. To address these challenges, we introduce Risk-aware Adaptive CBFs (RACBFs), which integrate Discrete-time Auxiliary-Variable adaptive CBFs (DAVCBFs) with coherent risk measures. DAVCBFs introduce auxiliary variables to improve the feasibility of the optimal control problem, while RACBFs incorporate risk-aware formulations to balance safety and risk evaluation performance. By extending discrete-time high-order CBF constraints over multiple steps, RACBFs effectively handle multi-step uncertainties that propagate through the system dynamics. We demonstrate the effectiveness of our approach on a stochastic unicycle system, showing that RACBFs maintain safety and feasibility while reducing unnecessary conservatism compared to standard robust formulations of discrete-time CBF methods.