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    Summary
    This summary is machine-generated.

    This study introduces adaptive optimal tracking for multiplayer nonlinear systems using adaptive critic learning. It ensures tracking errors remain within bounds, achieving a Nash equilibrium for multiple value functions.

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    Area of Science:

    • Control Systems Engineering
    • Artificial Intelligence
    • Game Theory

    Background:

    • Multiplayer nonlinear systems present complex control challenges.
    • Achieving optimal tracking with bounded errors is crucial for system performance.
    • Adaptive critic learning offers a powerful framework for complex control problems.

    Purpose of the Study:

    • To develop adaptive optimal prescribed performance tracking solutions for multiplayer nonlinear systems.
    • To constrain tracking errors within a predefined bounded set.
    • To utilize adaptive critic learning for achieving Nash equilibrium in value functions.

    Main Methods:

    • Decomposition of optimal tracking solutions into steady-state and adaptive feedback parts.
    • Application of adaptive critic learning with prescribed performance constraints.
    • Analysis of critic network weight convergence using the Lyapunov algorithm.

    Main Results:

    • The proposed method achieves adaptive optimal tracking for multiplayer nonlinear systems.
    • Tracking errors are successfully constrained to a predefined bounded set.
    • Simulation and experimental results validate the effectiveness of the approach.

    Conclusions:

    • The adaptive critic learning scheme provides effective solutions for optimal prescribed performance tracking.
    • The method ensures robust performance in multiplayer nonlinear systems.
    • The developed approach demonstrates satisfactory performance and convergence.