Myopically Verifiable Probabilistic Certificates for Safe Control and Learning
<|reference_start|>Myopically Verifiable Probabilistic Certificates for Safe Control and Learning: This paper addresses the design of safety certificates for stochastic systems, with a focus on ensuring long-term safety through fast real-time control. In stochastic environments, set invariance-based methods that restrict the probability of risk events in infinitesimal time intervals may exhibit significant long-term risks due to cumulative uncertainties/risks. On the other hand, reachability-based approaches that account for the long-term future may require prohibitive computation in real-time decision making. To overcome this challenge involving stringent long-term safety vs. computation tradeoffs, we first introduce a novel technique termed `probabilistic invariance'. This technique characterizes the invariance conditions of the probability of interest. When the target probability is defined using long-term trajectories, this technique can be used to design myopic conditions/controllers with assured long-term safe probability. Then, we integrate this technique into safe control and learning. The proposed control methods efficiently assure long-term safety using neural networks or model predictive controllers with short outlook horizons. The proposed learning methods can be used to guarantee long-term safety during and after training. Finally, we demonstrate the performance of the proposed techniques in numerical simulations.<|reference_end|>
@article{wang2024myopically,
    title={Myopically Verifiable Probabilistic Certificates for Safe Control and
  Learning},
    author={Zhuoyuan Wang, Haoming Jing, Christian Kurniawan, Albert Chern, Yorie
  Nakahira},
    journal={arXiv preprint arXiv:2404.16883},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.16883},
    primaryClass={eess.SY cs.LG cs.SY}
}