Myopically Verifiable Probabilistic Certificates for Safe Control and Learning

• URL: http://arxiv.org/abs/2404.16883v1
• Date: Tue, 23 Apr 2024 20:29:01 GMT
• Title: Myopically Verifiable Probabilistic Certificates for Safe Control and Learning
• Authors: Zhuoyuan Wang, Haoming Jing, Christian Kurniawan, Albert Chern, Yorie Nakahira,
• Abstract summary: In environments, set invariance-based methods that restrict the probability of risk events in infinitesimal time intervals may exhibit significant long-term risks. On the other hand, reachability-based approaches that account for the long-term future may require prohibitive in real-time decision making.
• Score: 7.6918726072590555
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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