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    Area of Science:

    • Control Systems Engineering
    • Nonlinear Dynamics
    • Fractional Calculus

    Background:

    • Iterative learning control (ILC) is crucial for repetitive tasks in linear time-invariant (LTI) systems.
    • Traditional ILC methods often face slow convergence rates, limiting their practical application.
    • Achieving high precision in ILC requires efficient and robust control strategies.

    Purpose of the Study:

    • To develop an accelerated iterative learning control scheme for LTI systems.
    • To enhance the convergence rate of tracking errors using a novel update rule.
    • To analyze the convergence properties of the proposed control scheme.

    Main Methods:

    • Implementation of a fractional high-order update rule (FHUR) with adaptive power terms for tracking errors.
    • Development of two optimal learning mechanisms for gain selection.
    • Application of a disturbed composite nonlinear mapping method for convergence analysis.

    Main Results:

    • The FHUR effectively accelerates convergence by utilizing high- and low-order power terms to manage large and small tracking errors.
    • Convergence analysis proved that tracking errors converge to an invariant set or limit cycles, depending on the learning mechanism.
    • The proposed FHUR demonstrated superior performance compared to the conventional proportional-type update rule in numerical simulations.

    Conclusions:

    • The fractional high-order update rule (FHUR) offers a promising approach for accelerated iterative learning control.
    • The developed control scheme achieves desired tracking precision by adjusting FHUR parameters.
    • This study provides a robust framework for enhancing ILC performance in LTI systems.