Stochastic Barrier Certificates in the Presence of Dynamic Obstacles
arXiv:2604.20208v2 Announce Type: replace Abstract: In this work, we focus on safety verification of stochastic systems in dynamic environments. We introduce both time-invariant and time-varying barrier certificates for discrete-time, continuous-space systems subject to uncertainty, which provide certified lower bounds on the probability of remaining within a safe set over a finite horizon. These certificates explicitly account for time-varying unsafe regions induced by obstacle dynamics. By le
Overview
arXiv:2604.20208v2 Announce Type: replace Abstract: In this work, we focus on safety verification of stochastic systems in dynamic environments. We introduce both time-invariant and time-varying barrier certificates for discrete-time, continuous-space systems subject to uncertainty, which provide certified lower bounds on the probability of remaining within a safe set over a finite horizon. These certificates explicitly account for time-varying unsafe regions induced by obstacle dynamics. By leveraging Bellman's optimality perspective, the time-varying formulation directly captures temporal structure and yields less conservative bounds than state-of-the-art approaches. By restricting certificates to polynomial functions, we show that time-varying barrier synthesis can be formulated as a convex sum-of-squares program, enabling tractable optimization. Empirical evaluations on nonlinear systems with dynamic obstacles show that time-varying certificates consistently achieve tight guarantees, demonstrating improved accuracy and scalability over state-of-the-art methods.
Source
Originally published at arxiv.org.
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Source: https://arxiv.org/abs/2604.20208