Stability of Time-Invariant Extremum Seeking Control for Limit Cycle Minimization

• 成果类型: Article
• 署名作者: Kumar, Saurav; Makarenkov, Oleg; Gregg, Robert D.; Gans, Nicholas
• 署名单位: Carnegie Mellon University; University of Texas System; University of Texas Dallas; University of Michigan System; University of Michigan; University of Texas System; University of Texas Arlington
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3181253
• 发表日期: 2022
• 页码: 5017-5024
• 关键词: Limit-cycles; Perturbation methods; asymptotic stability; oscillators; Time-frequency analysis; linear programming; detectors; Adaptive control; Autonomous systems; extremum seeking control; limit cycles; perturbation theory

摘要

This article presents a time-invariant extremum seeking controller (ESC) for nonlinear autonomous systems with limit cycles. For this time-invariant ESC, we propose a method to prove the closed-loop system has an asymptotically stable limit cycle. The method is based on a perturbation theorem for maps, and, unlike existing techniques that use averaging and singular perturbation tools, it is not limited to weakly nonlinear systems. We use a typical example system to show that our method does indeed establish asymptotic stability of the limit cycle with minimal amplitude. Utilizing the example, we provide a general guide for analytic computations that are required to apply our method. The corresponding Mathematica code is available as supplementary material.