A Framework for Safe Probabilistic Invariance Verification of Stochastic Dynamical Systems
Fuente:
arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911976358150144 |
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| author | Wu, Taoran Yu, Yiqing Xia, Bican Wang, Ji Xue, Bai |
| author_facet | Wu, Taoran Yu, Yiqing Xia, Bican Wang, Ji Xue, Bai |
| contents | Ensuring safety through set invariance has proven to be a valuable method in various robotics and control applications. This paper introduces a comprehensive framework for the safe probabilistic invariance verification of both discrete- and continuous-time stochastic dynamical systems over an infinite time horizon. The objective is to ascertain the lower and upper bounds of liveness probabilities for a given safe set and set of initial states. The liveness probability signifies the likelihood of the system remaining within the safe set indefinitely, starting from a state in the initial set. To address this problem, we propose optimizations for verifying safe probabilistic invariance in discrete-time and continuous-time stochastic dynamical systems. These optimizations are constructed via either using the Doob's nonnegative supermartingale inequality-based method or relaxing the equations described in [30,32], which can precisely characterize the probability of reaching a target set while avoiding unsafe states. Finally, we demonstrate the effectiveness of these optimizations through several examples using semi-definite programming tools. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09007 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Framework for Safe Probabilistic Invariance Verification of Stochastic Dynamical Systems Wu, Taoran Yu, Yiqing Xia, Bican Wang, Ji Xue, Bai Systems and Control Ensuring safety through set invariance has proven to be a valuable method in various robotics and control applications. This paper introduces a comprehensive framework for the safe probabilistic invariance verification of both discrete- and continuous-time stochastic dynamical systems over an infinite time horizon. The objective is to ascertain the lower and upper bounds of liveness probabilities for a given safe set and set of initial states. The liveness probability signifies the likelihood of the system remaining within the safe set indefinitely, starting from a state in the initial set. To address this problem, we propose optimizations for verifying safe probabilistic invariance in discrete-time and continuous-time stochastic dynamical systems. These optimizations are constructed via either using the Doob's nonnegative supermartingale inequality-based method or relaxing the equations described in [30,32], which can precisely characterize the probability of reaching a target set while avoiding unsafe states. Finally, we demonstrate the effectiveness of these optimizations through several examples using semi-definite programming tools. |
| title | A Framework for Safe Probabilistic Invariance Verification of Stochastic Dynamical Systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2404.09007 |