Strong Prescribed-Time Stabilization of Uncertain Nonlinear Systems by Periodic Delayed Feedback

• 成果类型: Article
• 署名作者: Ding, Yi; Zhou, Bin; Zhang, Kang-Kang; Michiels, Wim
• 署名单位: Harbin Institute of Technology; KU Leuven
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3347703
• 发表日期: 2024
• 页码: 4072-4079
• 关键词: High-order nonlinear systems; periodic delayed feedback (PDF); prescribed-time stabilization; strong prescribed-time stabilization

摘要

In this article, a novel Lyapunov-based approach for strong prescribed-time stabilization by periodic delayed feedback is established. Since the comparison lemma cannot be directly applied to time-delay systems, their proofs rely on trajectory analysis. Based on this approach, a novel control law for strong prescribed-time stabilization of uncertain scalar nonlinear systems is obtained, with the following appealing properties: singularity problems inherent to time-varying high gain approaches are avoided; strong prescribed-time stabilization is achieved with control terms exhibiting a linear growth rate in the combined current and delayed state variable; the achieved fixed-time stability is preserved under classes of additive perturbations; and the setting time of the closed-loop system equals the prescribed value for some admissible uncertainties. Subsequently, using the backstepping procedure, a strongly prescribed-time stabilizing control law for strict feedback uncertain nonlinear systems is designed. Numerical simulations are shown to verify the effectiveness of the proposed approaches.