Converse Barrier Certificates for Finite-time Safety Verification of Continuous-time Perturbed Deterministic Systems
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909986079113216 |
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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 |