Runtime Safety and Reach-avoid Prediction of Stochastic Systems via Observation-aware Barrier Functions

Stochastic dynamical systems have emerged as fundamental models across numerous application domains, providing powerful mathematical representations for capturing uncertain system behavior. In this paper, we address the problem of runtime safety and reach-avoid probability prediction for discrete-time stochastic systems with online observations, i.e., estimating the probability that the system satisfies a given safety or reach-avoid specification. Unlike traditional approaches that rely solely on offline models, we propose a framework that incorporates real-time observations to dynamically refine probability estimates for safety and reach-avoid events. By introducing observation-aware barrier functions, our method adaptively updates probability bounds as new observations are collected, combining efficient offline computation with online backward iteration. This approach enables rigorous and responsive prediction of safety and reach-avoid probabilities under uncertainty. In addition to the theoretical guarantees, experimental results on benchmark systems demonstrate the practical effectiveness of the proposed method.

Authors

• Shenghua Feng National Key Laboratory of Space Integrated Information System, Institute of Software Chinese Academy of Sciences, Beijing, China University of Chinese Academy of Sciences, Beijing, China
• Jie An
• Fanjiang Xu Institute of Software Chinese Academy of Sciences, Beijing, China Science & Technology on Integrated Information System Laboratory, Beijing, China State Key Laboratory of Intelligent Game, Beijing, China University of Chinese Academy of Sciences, Beijing, China

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