Reach-Avoid Certificates for Contact-based Stochastic Hybrid Systems

arXiv:2610.17308v1 Announce Type: cross Abstract: This work studies certified reach-avoid control of stochastic hybrid systems in which a stochastic differential equation governs continuous flow and a controlled stochastic kernel governs guard-triggered resets. The input appears only in the reset kernel, where it determines the post-jump distribution. Certificates for such systems have so far assumed spontaneous or controller-chosen jump times, a finite horizon, or discrete-time dynamics; we certify, over the infinite horizon, that the target is reached before the unsafe set with at least a prescribed probability. First, we introduce reach-avoid contact certificates, whose flow and jump conditions are imposed only on a sublevel corridor, and prove that any such certificate with a compatible reset policy meets the specification; a pointwise safety filter extends this guarantee from verification to control by constraining arbitrary nominal controllers. Next, we prove that executions are non-Zeno and bound the expected settling time and reset count. We frame certificate search as a linear program over any twice-differentiable dictionary followed by independent verification. We illustrate our approach via comparisons where the certified region is a subset covering 93.6\% of the ground truth and where our certificate-based safety filter reaches the goal while reducing collisions from 68 to zero across 200 episodes of a dribbling ball problem.

Abstract:This work studies certified reach-avoid control of stochastic hybrid systems in which a stochastic differential equation governs continuous flow and a controlled stochastic kernel governs guard-triggered resets. The input appears only in the reset kernel, where it determines the post-jump distribution. Certificates for such systems have so far assumed spontaneous or controller-chosen jump times, a finite horizon, or discrete-time dynamics; we certify, over the infinite horizon, that the target is reached before the unsafe set with at least a prescribed probability. First, we introduce reach-avoid contact certificates, whose flow and jump conditions are imposed only on a sublevel corridor, and prove that any such certificate with a compatible reset policy meets the specification; a pointwise safety filter extends this guarantee from verification to control by constraining arbitrary nominal controllers. Next, we prove that executions are non-Zeno and bound the expected settling time and reset count. We frame certificate search as a linear program over any twice-differentiable dictionary followed by independent verification. We illustrate our approach via comparisons where the certified region is a subset covering 93.6\% of the ground truth and where our certificate-based safety filter reaches the goal while reducing collisions from 68 to zero across 200 episodes of a dribbling ball problem.

Systems and Control (eess.SY); Robotics (cs.RO); Probability (math.PR)

arXiv:2610.17308 [eess.SY]

(or arXiv:2610.17308v1 [eess.SY] for this version)

https://doi.org/10.48550/arXiv.2610.17308 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Reach-Avoid Certificates for Contact-based Stochastic Hybrid Systems

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