Hybrid Safety Verification of Multi-Agent Systems using $ψ$-Weighted CBFs and PAC Guarantees

Abstract--This study proposes a hybrid safety verification framework for closed-loop multi-agent systems under bounded stochastic disturbances. The proposed approach augments control barrier functions with a novel ψ-weighted formulation that encodes directional control alignment between agents into the safety constraints. Deterministic admissibility is combined with empirical validation via Monte Carlo rollouts, and a PAC-style guarantee is derived based on margin-aware safety violations to provide a probabilistic safety certificate. The results from the experiments conducted under different bounded stochastic disturbances validate the feasibility of the proposed approach. Safety within multi-agent systems is essential for real-world applications such as autonomous driving [1], [2] and robotic swarm deployments in agriculture [3], [4], manufacturing [5], [6], and search and rescue operations [7], where agents must navigate safely through their environment.