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    This study introduces a fully distributed adaptive Nash equilibrium for multiagent systems, enabling agents to synchronize with a leader while optimizing performance using only local information. This approach enhances control in complex networks.

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    Area of Science:

    • Control Theory
    • Game Theory
    • Networked Systems

    Background:

    • Multiagent systems require coordinated control for tasks like synchronization.
    • Existing solutions often rely on global information, limiting scalability.
    • Differential graphical games offer a framework for analyzing decentralized control.

    Purpose of the Study:

    • To develop a fully distributed Nash equilibrium solution for linear multiagent systems with a leader.
    • To ensure agents synchronize with the leader while optimizing a performance index.
    • To analyze the stability and equilibrium properties of the proposed solution.

    Main Methods:

    • Formulating a differential graphical game for leader-following multiagent systems.
    • Designing a distributed adaptive control law based on local information.
    • Analyzing asymptotic stability and global Nash equilibrium properties.

    Main Results:

    • A novel fully distributed adaptive Nash equilibrium solution was proposed.
    • The solution enables agents to synchronize with the leader using only local information.
    • Asymptotic stability and global Nash equilibrium were proven for the proposed solution.

    Conclusions:

    • The proposed method achieves leader synchronization and performance optimization in a fully distributed manner.
    • The approach is applicable to real-world problems, such as microgrid secondary control.
    • This work advances the field of decentralized control for networked systems.