Synthesis and Deployment of Maximal Robust Control Barrier Functions through Adversarial Reinforcement Learning

• URL: http://arxiv.org/abs/2604.13192v1
• Date: Tue, 14 Apr 2026 18:16:17 GMT
• Title: Synthesis and Deployment of Maximal Robust Control Barrier Functions through Adversarial Reinforcement Learning
• Abstract summary: We introduce a new robust CBF framework for general nonlinear systems under bounded uncertainty.<n>We first show that the safety value function solving the dynamic programming Isaacs equation is a valid robust discrete-time CBF that enforces safety on the maximal robust safe set.<n>We then adopt the key reinforcement learning notion of quality function (RL) which removes the need for explicit dynamics by lifting the barrier certificate into state-action space.
• Score: 4.062182903323153
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Robust control barrier functions (CBFs) provide a principled mechanism for smooth safety enforcement under worst-case disturbances. However, existing approaches typically rely on explicit, closed-form structure in the dynamics (e.g., control-affine) and uncertainty models. This has led to limited scalability and generality, with most robust CBFs certifying only conservative subsets of the maximal robust safe set. In this paper, we introduce a new robust CBF framework for general nonlinear systems under bounded uncertainty. We first show that the safety value function solving the dynamic programming Isaacs equation is a valid robust discrete-time CBF that enforces safety on the maximal robust safe set. We then adopt the key reinforcement learning (RL) notion of quality function (or Q-function), which removes the need for explicit dynamics by lifting the barrier certificate into state-action space and yields a novel robust Q-CBF constraint for safety filtering. Combined with adversarial RL, this enables the synthesis and deployment of robust Q-CBFs on general nonlinear systems with black-box dynamics and unknown uncertainty structure. We validate the framework on a canonical inverted pendulum benchmark and a 36-D quadruped simulator, achieving substantially less conservative safe sets than barrier-based baselines on the pendulum and reliable safety enforcement even under adversarial uncertainty realizations on the quadruped.

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