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    Area of Science:

    • Control Systems Engineering
    • Nonlinear Dynamics
    • Distributed Systems

    Background:

    • The distributed average tracking (DAT) problem is crucial for coordinating multiple agents.
    • Existing asymptotic DAT algorithms may not guarantee convergence within a specific timeframe.
    • Handling multiple, time-varying reference signals in nonlinear systems presents significant challenges.

    Purpose of the Study:

    • To develop novel distributed average tracking algorithms for second-order nonlinear systems.
    • To achieve finite-time convergence for agent states to the average of reference signals.
    • To design a fully distributed DAT algorithm that does not require global information.

    Main Methods:

    • Utilizing state-dependent gain design and adaptive control techniques.
    • Developing a finite-time DAT algorithm with a Lyapunov function for settling time estimation.
    • Designing an adaptive-gain DAT algorithm for fully distributed implementation.

    Main Results:

    • The finite-time DAT algorithm ensures agent states track the average of time-varying reference signals within a finite settling time.
    • The finite settling time is estimated and bounded using a designed Lyapunov function.
    • The adaptive-gain DAT algorithm achieves distributed average tracking without requiring global system information.

    Conclusions:

    • The proposed finite-time DAT algorithm offers superior performance over asymptotic methods by guaranteeing finite-time convergence.
    • The adaptive-gain DAT algorithm provides a fully distributed solution, enhancing practical applicability.
    • Numerical simulations validate the effectiveness and accuracy of both developed DAT algorithms.