Fixed-Time Gradient Dynamics With Time-Varying Coefficients for Continuous-Time Optimization

• 成果类型: Article
• 署名作者: Nguyen, Lien T. T.; Yu, Xinghuo; Eberhard, Andrew; Li, Chaojie
• 署名单位: Royal Melbourne Institute of Technology (RMIT); Royal Melbourne Institute of Technology (RMIT); University of New South Wales Sydney
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3206251
• 发表日期: 2023
• 页码: 4383-4390
• 关键词: Continuous-time optimization; fixed-time convergence; gradient-based method; Lyapunov function; Newton-like method; STABILITY; Time-varying systems

摘要

In this article, we propose fixed-time gradient dynamics with time-varying coefficients for continuous-time optimization. We first investigate the Lyapunov stability conditions that allow us to achieve fixed-time stability of the time-varying dynamical systems. We then use them to deal with continuous-time optimization problems. We show that under the proposed fixed-time gradient dynamics and by choosing time-varying coefficients, the searching trajectories converge to their optima in fixed-time from any initial points with a very fast rate. Simulation results are given to show the effectiveness of the proposed fixed-time gradient dynamics with tunable time-varying coefficients for continuous-time optimization.