Probabilistic Safety Certificate for Multi-agent Systems.

This paper focuses on the multi-agent safe control problem for stochastic systems. We propose a probabilistic certificate for safety and performance specifications and use it to construct a distributed algorithm. The certificate integrates the reachability- and invariance-based (barrier-function-based) approaches via a new notion of forward invariance defined on the long-term probability. The proposed method has two features. First, it can guarantee a long-term probability of safety and performance satisfaction using myopic evaluation. Second, each agent can collaboratively ensure system-wide specifications even if each does not have sufficient information to evaluate the specifications. The effectiveness of the proposed method is tested using numerical experiments.