Refined Barrier Conditions for Finite-Time Safety and Reach-Avoid Guarantees in Stochastic Systems
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909032161214464 |
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| author | Xue, Bai Ong, Luke Wagner, Dominik Wang, Peixin |
| author_facet | Xue, Bai Ong, Luke Wagner, Dominik Wang, Peixin |
| contents | Providing finite-time probabilistic safety and reach-avoid guarantees is crucial for safety-critical stochastic systems. Existing state-of-the-art barrier methods often rely on a restrictive boundedness assumption for auxiliary functions, limiting their applicability. This paper presents refined barrier conditions that remove this assumption. Specifically, we establish conditions for deriving upper bounds on finite-time safety probabilities in discrete-time systems and lower bounds on finite-time reach-avoid probabilities in continuous-time systems. This relaxation expands the class of verifiable systems, especially those with unbounded state spaces, and facilitates the use of advanced optimization techniques, such as semi-definite programming with polynomial functions. Numerical examples demonstrate the effectiveness of the approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18518 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Refined Barrier Conditions for Finite-Time Safety and Reach-Avoid Guarantees in Stochastic Systems Xue, Bai Ong, Luke Wagner, Dominik Wang, Peixin Systems and Control Providing finite-time probabilistic safety and reach-avoid guarantees is crucial for safety-critical stochastic systems. Existing state-of-the-art barrier methods often rely on a restrictive boundedness assumption for auxiliary functions, limiting their applicability. This paper presents refined barrier conditions that remove this assumption. Specifically, we establish conditions for deriving upper bounds on finite-time safety probabilities in discrete-time systems and lower bounds on finite-time reach-avoid probabilities in continuous-time systems. This relaxation expands the class of verifiable systems, especially those with unbounded state spaces, and facilitates the use of advanced optimization techniques, such as semi-definite programming with polynomial functions. Numerical examples demonstrate the effectiveness of the approach. |
| title | Refined Barrier Conditions for Finite-Time Safety and Reach-Avoid Guarantees in Stochastic Systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2509.18518 |