Risk-Aware Stability, Ultimate Boundedness, and Positive Invariance

• 成果类型: Article
• 署名作者: Kishida, Masako
• 署名单位: Research Organization of Information & Systems (ROIS); National Institute of Informatics (NII) - Japan
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3301817
• 发表日期: 2024
• 页码: 681-688
• 关键词: Conditional value-at-risk; event-triggered control; positive invariance; STABILITY; Stochastic systems; ultimate boundedness

摘要

This article introduces the notions of stability, ultimate boundedness, and positive invariance for stochastic systems in view of risk. More specifically, those notions are defined in terms of the worst-case conditional value-at-risk (CVaR), which quantifies the worst-case conditional expectation of losses exceeding a certain threshold over a set of possible uncertainties. Those notions allow us to focus our attention on the tail behavior of stochastic systems in the analysis of dynamical systems and the design of controllers. Furthermore, some event-triggered control strategies that guarantee ultimate boundedness and positive invariance with specified bounds are derived using the obtained results and illustrated using numerical examples.