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Iterative Learning Control for Discrete-Time Systems With Full Learnability.

Jian Liu, Xiaoe Ruan, Yuanshi Zheng

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    This summary is machine-generated.

    Iterative learning control (ILC) for discrete-time systems is analyzed. A new framework links system learnability to the input-output coupling matrix (IOCM), ensuring monotone convergence with state feedback.

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    Area of Science:

    • Control Engineering
    • Systems Theory
    • Applied Mathematics

    Background:

    • Iterative Learning Control (ILC) is crucial for systems performing repetitive tasks.
    • Analyzing learnability and unknown dynamics in discrete-time systems presents challenges.
    • The Input-Output Coupling Matrix (IOCM) plays a key role in system behavior.

    Purpose of the Study:

    • To develop a framework for analyzing the learnability of discrete-time control systems.
    • To design data-based learning schemes for unknown system dynamics.
    • To guarantee monotone convergence of the ILC process using state feedback.

    Main Methods:

    • Establishing a relationship between system learnability and the IOCM.
    • Developing data-based learning schemes utilizing system repetitiveness.
    • Designing iterative learning and state feedback gain matrices based on system dynamics.
    • Proving convergence using the IOCM's full-row rank property.

    Main Results:

    • Full learnability is achieved if and only if the IOCM is full-row rank.
    • Data-based schemes can extract system dynamics information if the system is controllable.
    • The proposed ILC scheme with state feedback guarantees monotone convergence under specific conditions.

    Conclusions:

    • The study provides a robust framework for analyzing and designing ILC systems.
    • The proposed method effectively handles unknown dynamics and ensures convergence.
    • Numerical validation confirms the practical applicability of the developed ILC scheme.