Certifiable Deep Learning for Reachability Using a New Lipschitz Continuous Value Function
<|reference_start|>Certifiable Deep Learning for Reachability Using a New Lipschitz Continuous Value Function: 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 any disturbance within pre-specified bounds. Our framework has two main parts: offline learning of a newly designed reach-avoid value function and post-learning certification. Compared to prior works, 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 takeover example.<|reference_end|>
@article{li2024certifiable,
    title={Certifiable Deep Learning for Reachability Using a New Lipschitz
  Continuous Value Function},
    author={Jingqi Li, Donggun Lee, Jaewon Lee, Kris Shengjun Dong, Somayeh
  Sojoudi, Claire Tomlin},
    journal={arXiv preprint arXiv:2408.07866},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.07866},
    primaryClass={eess.SY cs.SY}
}