Almost Sure Safety Analysis and Safety-Critical Control of Stochastic Systems

This paper is concerned with almost-sure safety guarantee problems for Ito-type stochastic systems. By introducing composite barrier functions, almost-sure safety certificates are first established, which not only parallel safety verifications based on zeroing barrier functions in deterministic systems but also differ from the existing studies that primarily focus on computing the upper probability of stochastic systems exiting a predefined safe region within the state space. Subsequently, the relation-ship between safety and stability and the safety-critical control problem of stochastic systems are further discussed, respectively. Academic examples are used to illustrate the theoretical results.