Certifiable Reachability Learning Using a New Lipschitz Continuous Value Function
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909495163092992 |
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| author | Li, Jingqi Lee, Donggun Lee, Jaewon Dong, Kris Shengjun Sojoudi, Somayeh Tomlin, Claire |
| author_facet | Li, Jingqi Lee, Donggun Lee, Jaewon Dong, Kris Shengjun Sojoudi, Somayeh Tomlin, Claire |
| contents | We propose a new reachability learning framework for high-dimensional nonlinear systems, focusing on reach-avoid problems. These problems require computing the reach-avoid set, which ensures that all its elements can safely reach a target set despite disturbances within pre-specified bounds. Our framework has two main parts: offline learning of a newly designed reachavoid value function, and post-learning certification. Compared to prior work, our new value function is Lipschitz continuous and its associated Bellman operator is a contraction mapping, both of which improve the learning performance. To ensure deterministic guarantees of our learned reach-avoid set, we introduce two efficient post-learning certification methods. Both methods can be used online for real-time local certification or offline for comprehensive certification. We validate our framework in a 12-dimensional crazyflie drone racing hardware experiment and a simulated 10-dimensional highway take-over example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_07866 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Certifiable Reachability Learning Using a New Lipschitz Continuous Value Function Li, Jingqi Lee, Donggun Lee, Jaewon Dong, Kris Shengjun Sojoudi, Somayeh Tomlin, Claire Systems and Control We propose a new reachability learning framework for high-dimensional nonlinear systems, focusing on reach-avoid problems. These problems require computing the reach-avoid set, which ensures that all its elements can safely reach a target set despite disturbances within pre-specified bounds. Our framework has two main parts: offline learning of a newly designed reachavoid value function, and post-learning certification. Compared to prior work, our new value function is Lipschitz continuous and its associated Bellman operator is a contraction mapping, both of which improve the learning performance. To ensure deterministic guarantees of our learned reach-avoid set, we introduce two efficient post-learning certification methods. Both methods can be used online for real-time local certification or offline for comprehensive certification. We validate our framework in a 12-dimensional crazyflie drone racing hardware experiment and a simulated 10-dimensional highway take-over example. |
| title | Certifiable Reachability Learning Using a New Lipschitz Continuous Value Function |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2408.07866 |