Upper Bound on Escape Probability for Stochastic Control Barrier Functions
成果类型：
Article
署名作者：
Jang, Inkyu; Kim, H. Jin
署名单位：
Seoul National University (SNU)
刊物名称：
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
ISSN/ISSBN：
0018-9286
DOI：
10.1109/TAC.2025.3638059
发表日期：
2026
关键词：
摘要：
This article introduces a new upper bound on the escape probability of a stochastic system from a super zero level set of a zeroing-type stochastic control barrier function (SCBF). For both discrete-time and continuous-time cases, a time-varying probability bound is built by constructing a supermartingale and then applying Ville's inequality. While existing martingale-based probability bounds depend only on the expectation of change of the SCBF value, the proposed bound also takes into account the growth rate of its variance, resulting in enhanced tightness. The construction of the proposed bound does not require the SCBF value to be globally bounded; thus, it is more suitable for tasks with large and noncompact safe sets. The validity and tightness of the proposed bound are checked using Monte Carlo simulation experiments.