Accelerating Iterative Learning Control Using Fractional-Proportional-Type Update Rule

• 成果类型: Article
• 署名作者: Li, Zihan; Shen, Dong; Yu, Xinghuo
• 署名单位: Renmin University of China; Renmin University of China; Royal Melbourne Institute of Technology (RMIT)
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3488813
• 发表日期: 2025
• 页码: 2706-2713
• 关键词: convergence; Perturbation methods; Sliding mode control; Numerical simulation; Iterative learning control; uncertainty; nonlinear dynamical systems; noise; Lyapunov methods; indexes; Asymptotic convergence; convergence rate; fractional-proportional-type update rule (FPUR); nonlinear recursion

摘要

Using the proportional-type update rule (PTUR) is the most common update approach for iterative learning control. By combining PTUR and a newly proposed fractional-power-type update rule (FTUR), a fractional-proportional-type update rule is proposed to achieve fast convergence for scenarios where the tracking errors can be large or small. The nonlinearity of fractional power term and tracking error accumulation along the time axis introduce considerable challenges in convergence analysis and convergence rate estimation. Thus, a novel analysis method is proposed for nonlinear recursion with perturbation where the convergence is established as per nonlinear tracking-error dynamics. The limits of the tracking errors are demonstrated independent of the system matrices. The relationship between the convergence limit and initial tracking error is examined. Moreover, the local and global convergence rates are provided. The proposed approach exhibits an advantage in terms of the convergence rate compared with PTUR and FTUR. Optimal parameter selection is achieved based on the convergence rate. The theoretical results are confirmed via numerical simulations.