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

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 $\psi$-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.