Bounded Extremum Seeking for Static Quadratic Maps Using Nonlinear Transformation and Lyapunov Method

• 成果类型: Article
• 署名作者: Mazenc, Frederic; Malisoff, Michael; Fridman, Emilia
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Louisiana State University System; Louisiana State University; Tel Aviv University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3504356
• 发表日期: 2025
• 关键词: stability; DESIGN

摘要

We present a new practical stability analysis for a bounded gradient based extremum seeking problem for two variable static quadratic maps that contain a time-varying additive measurement uncertainty. Instead of using earlier averaging-based approaches, we introduce a new state transformation, a time-varying quadratic Lyapunov function, and a comparison principle to obtain essentially less conservative bounds on the dither frequency and on the ultimate bound of the estimation error compared with earlier results. Our numerical example illustrates the efficiency of the method.