Extremum-Seeking Control for a Class of Mechanical Systems

• 成果类型: Article
• 署名作者: Suttner, Raik
• 署名单位: University of Wurzburg
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3148377
• 发表日期: 2023
• 页码: 1200-1207
• 关键词: Mechanical systems; Closed loop systems; asymptotic stability; linear programming; kinematics; Stability criteria; Perturbation methods; averaging; extremum-seeking control; mechanical systems; practical stability; symmetric products

摘要

We present a novel extremum-seeking method for affine connection mechanical control systems. The proposed control law involves periodic perturbation signals with sufficiently large amplitudes and frequencies. A suitable averaging analysis reveals that the solutions of the closed-loop system converge locally uniformly to the solutions of an averaged system in the large-amplitude high-frequency limit. This in turn leads to the effect that stability properties of the averaged system carry over to the approximating closed-loop system. Descent directions of the objective function are given by symmetric products of vector fields in the averaged system. Under suitable assumptions, we prove that minimum points of the objective function are asymptotically stable for the averaged system and therefore practically asymptotically stable for the closed-loop system. We illustrate our results by examples and numerical simulations.