接触を伴う確率ハイブリッドシステムのための到達回避証明
Reach-Avoid Certificates for Contact-based Stochastic Hybrid Systems
確率微分方程式と制御されたリセットカーネルからなる確率ハイブリッドシステムに対し、無限ホライズンで目標到達と危険回避を保証する証明と安全フィルタを提案した。
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著者: Tianyi Xia, Ryan K. Cosner
分類: eess.SY, cs.RO, math.PR
原文アブストラクト
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.
