Extremum Seeking Feedback Under Unknown Hessian Signs

• 成果类型: Article
• 署名作者: Dibo, Aline; Oliveira, Tiago Roux
• 署名单位: Universidade do Estado do Rio de Janeiro
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3306453
• 发表日期: 2024
• 页码: 2383-2390
• 关键词: Monitoring; switches; mathematical models; Upper bound; Real-time systems; Perturbation methods; optimization; Adaptive control; extremum seeking (ES); switching monitoring function; uncertain nonlinear systems

摘要

Extremum seeking control aims at determining and keeping the output of a nonlinear static or dynamic map on its unknown extremum point. In the literature, despite considering an unknown objective function in the real-time optimization problem, it is mandatory to know whether the extremum point is a maximum or a minimum, which is characterized by means of the Hessian sign of the nonlinear scalar map. This article proposes that the process of extremum seeking occurs independently of the Hessian sign information. The key idea is to combine the classical extremum seeking approach with a switching monitoring function-based scheme. The switching algorithm will drive the closed-loop system to the unknown extremum, neglecting if it is a maximum or a minimum equilibrium point. Theoretical results are rigorously justified and simulation examples show the robustness properties of the proposed recipe even when the changes of the Hessian sign occur in on-the-fly fashion, showing the adaptability of the proposed method to solve distinct online minimizing and maximizing problems in sequence.