Grid-Free Computation of Probabilistic Safety With Malliavin Calculus

• 成果类型: Article
• 署名作者: Cosentino, Francesco; Oberhauser, Harald; Abate, Alessandro
• 署名单位: University of Oxford; Alan Turing Institute; University of Oxford
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3239460
• 发表日期: 2023
• 页码: 6369-6376
• 关键词: Formal verification; Stochastic processes

摘要

This article concerns continuous-time, continuous-space stochastic dynamical systems described by stochastic differential equations (SDE). It presents a new approach to compute probabilistic safety regions, namely sets of initial conditions of the SDE associated to trajectories that are safe with a probability larger than a given threshold. The approach introduces a functional that is minimized at the border of the probabilistic safety region, then solves an optimization problem using techniques from Malliavin Calculus, which computes such region. Unlike existing results in the literature, the new approach allows one to compute probabilistic safety regions without gridding the state space of the SDE.