Adaptive Stabilization of Uncertain Linear System With Stochastic Delay by PDE Full-State Feedback

• 成果类型: Article
• 署名作者: Zhang, Zhengqiang; Fang, Qin; Chen, Xinkai
• 署名单位: Qufu Normal University; Shibaura Institute of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3306455
• 发表日期: 2024
• 页码: 2437-2444
• 关键词: adaptive control; prediction-based control; stochastic Barbalat's lemma; stochastic delay; uncertain linear systems

摘要

This article focuses on the equilibrium regulation problem of a class of uncertain linear systems with stochastic input delay, where the delay is modeled as a Markov process with finite states. Our approach is based on the partial differential equation backstepping method. We first consider the Markov delay with finite known states. An adaptive controller is designed to achieve global almost sure asymptotic convergence. Then, the Markov delay with finite unknown states is discussed. Owing to the unknown Markov delay resulting in the single distributed actuator state being unmeasured, the update law is redesigned, and only the local almost sure asymptotic stability is proved. In the control design, we adopt a constant-time-horizon-prediction-based control law to robustly compensate for the stochastic delay, which requires that the constant be close enough to all the Markov process states. Then, through Lyapunov functional analysis, we prove the almost sure boundedness of all the signals. Moreover, stochastic Barbalat's lemma is applied to realize equilibrium regulation. Finally, to show the effectiveness of our results, a numerical example is given.