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    A new data-driven optimal iterative learning control method enhances performance for nonlinear systems using past data. This approach improves tracking and transient response without needing system models, offering reduced complexity and proven convergence.

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    Area of Science:

    • Control Engineering
    • Systems Science
    • Data-Driven Control

    Background:

    • Repetitive control systems are crucial for tasks requiring high precision over repeated cycles.
    • Traditional methods often rely on accurate system models, limiting their applicability.
    • Improving online control performance and transient response remains a key challenge.

    Purpose of the Study:

    • To propose a novel data-driven higher order optimal iterative learning control (DDHOILC) for nonlinear repetitive discrete-time systems.
    • To enhance online control performance and transient response by leveraging historical and current iteration data.
    • To reduce computational complexity and eliminate the need for explicit system models.

    Main Methods:

    • A nonlifted iterative dynamic linearization formulation is employed.
    • Historical tracking errors and control inputs from previous iterations are utilized.
    • Current iteration's past time-instant data informs control input adjustments.
    • Data-driven approach relies solely on input-output data, avoiding model identification.

    Main Results:

    • The proposed DDHOILC method effectively enhances online control performance and transient response.
    • Computational complexity is reduced due to the avoidance of matrix inversion.
    • Rigorous mathematical proof demonstrates asymptotic convergence of the control law.
    • Higher-order learning control laws show superior convergence compared to lower-order ones.

    Conclusions:

    • The DDHOILC approach provides an effective, model-free solution for nonlinear repetitive systems.
    • The method offers improved performance and computational efficiency.
    • Simulation results validate the practical effectiveness and convergence properties of the proposed control strategy.