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

Fuente: arXiv
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Main Authors: Li, Yonghan, Wu, Chenyu, Wu, Taoran, Wang, Shijie, Xue, Bai
Format: Preprint
Published: 2024
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author Li, Yonghan
Wu, Chenyu
Wu, Taoran
Wang, Shijie
Xue, Bai
author_facet Li, Yonghan
Wu, Chenyu
Wu, Taoran
Wang, Shijie
Xue, Bai
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2402_17167
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Converse Barrier Certificates for Finite-time Safety Verification of Continuous-time Perturbed Deterministic Systems
Li, Yonghan
Wu, Chenyu
Wu, Taoran
Wang, Shijie
Xue, Bai
Systems and Control
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.
title Converse Barrier Certificates for Finite-time Safety Verification of Continuous-time Perturbed Deterministic Systems
topic Systems and Control
url https://arxiv.org/abs/2402.17167