Safety Assurance of Stochastic Systems

Safety is a critical requirement for real-world systems, including autonomous vehicles, robots, power grids and more. Over the past decades, many methods have been developed for safety verification and safe control design in deterministic systems. However, real-world applications often involve not only worst-case deterministic disturbances but also stochastic uncertainties, rendering deterministic methods insufficient. In this talk, I will present an effective framework that addresses this challenge by decoupling the effects of stochastic and deterministic disturbances. At the heart of this framework is a novel technique that provides probabilistic bounds on the deviation between the trajectories of stochastic systems and their deterministic counterparts with high confidence. This approach yields a tight probabilistic bound that is applicable to both continuous-time and discrete-time systems. By leveraging this bound, the safety verification problem for stochastic systems can be reduced to a deterministic one, enabling the use of existing deterministic methods to solve problems involving stochastic uncertainties. I will demonstrate the effectiveness of this framework through several safety verification and safe control tasks.