Stochastic System Safety: Probabilistic Invariance Verification
Set invariance has emerged as a powerful framework for safety assurance in robotics and control applications. This talk will introduce our methods for probabilistic invariance verification of stochastic dynamical systems, encompassing both discrete- and continuous-time cases over infinite time horizons. Our primary objective is to compute rigorous lower and upper bounds for safety probabilities, defined as the likelihood that a system remains indefinitely within a specified safe set when initialized from given starting states. We develop two verification approaches: one leveraging Doob’s nonnegative supermartingale inequality, and another based on relaxed formulations of our prior theoretical results. The proposed techniques are implemented using semidefinite programming tools, with numerical case studies demonstrating their practical efficacy in safety verification tasks.