Stochastic Barrier Certificates in the Presence of Dynamic Obstacles

• URL: http://arxiv.org/abs/2604.20208v1
• Date: Wed, 22 Apr 2026 05:49:35 GMT
• Title: Stochastic Barrier Certificates in the Presence of Dynamic Obstacles
• Abstract summary: This paper studies safety of dynamic systems in environments with dynamic obstacles through the lens of barrier functions.<n>We introduce both time-in and time-varying barrier certificates for discrete-time, continuous-space systems subject to uncertainty.<n>We show that time-varying certificates consistently achieve tight guarantees, demonstrating improved accuracy and scalability over state-of-the-art methods.
• Score: 13.052212457121295
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Safety of stochastic dynamic systems in environments with dynamic obstacles is studied in this paper through the lens of stochastic barrier functions. 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.

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