aiqbench analysis
This research advances AI safety by introducing time-varying stochastic barrier certificates capable of verifying systems in dynamic environments with moving obstacles. By formulating the synthesis problem as a convex optimization task, the method provides tighter probabilistic safety guarantees than existing approaches for nonlinear stochastic systems. The work directly addresses critical challenges in deploying autonomous agents where uncertainty and environmental dynamics must be rigorously bounded.
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 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.
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.
Robotics (cs.RO); Probability (math.PR)
arXiv:2604.20208 [cs.RO]
(or arXiv:2604.20208v2 [cs.RO] for this version)
https://doi.org/10.48550/arXiv.2604.20208 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 219 words
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