Reach-Avoid Certificates for Contact-based Stochastic Hybrid Systems

Key points

• 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.1
• 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.1
• We frame certificate search as a linear program over any twice-differentiable dictionary followed by independent verification.1
• 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.1

Sources (1)

• [1]Reach-Avoid Certificates for Contact-based Stochastic Hybrid Systems
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 12, 07:04 PM

  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.

  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.

Extractive summary: sentences quoted from the sources.