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arXiv · 2402.17167

Converse Barrier Certificates for Finite-time Safety Verification of Continuous-time Perturbed Deterministic Systems

Yonghan Li·Chenyu Wu·Taoran Wu·Shijie Wang·Bai Xue
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Abstract

In this paper, we investigate the problem of verifying the finite-time safety of continuous-time perturbed deterministic systems represented by ordinary differential equations in the presence of measurable disturbances. Given a finite-time horizon, if the system is safe, it, starting from a compact initial set, will remain within an open and bounded safe region throughout the specified time horizon, regardless of the disturbances. The main contribution of this work is a converse theorem: we prove that a continuously differentiable, time-dependent barrier certificate exists if and only if the system is safe over the finite-time horizon. The existence problem is explored by finding a continuously differentiable approximation of a unique Lipschitz viscosity solution to a Hamilton-Jacobi equation.

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Yonghan Li, Chenyu Wu, Taoran Wu, Shijie Wang, Bai Xue. 2026-01-11. Converse Barrier Certificates for Finite-time Safety Verification of Continuous-time Perturbed Deterministic Systems. https://arxiv.org/abs/2402.17167

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