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    This study introduces a federated learning adaptive dynamic programming (FL-ADP) control scheme for massive multiagent systems. The novel approach ensures stable optimal consensus control by approximating agent interactions using mean-field games (MFGs).

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    Area of Science:

    • Control Theory
    • Artificial Intelligence
    • Distributed Systems

    Background:

    • Massive multiagent systems face challenges in achieving real-time optimal consensus control due to numerous interactions and conflicts.
    • Existing methods struggle with the complexity and scale of these systems, necessitating advanced control strategies.

    Purpose of the Study:

    • To develop a novel federated learning adaptive dynamic programming (FL-ADP) control scheme for optimal consensus in massive multiagent systems.
    • To address the challenges posed by large-scale agent interactions and conflicts of interest.
    • To solve mean-field games (MFGs)-based optimal consensus problems.

    Main Methods:

    • Approximation of individual agent interactions using mean-field games (MFGs).
    • Development of a novel undiscounted performance index function incorporating mean-field coupling and tracking errors.
    • Utilization of a critic-mass neural network to solve coupled Hamilton-Jacobi-Bellman and Fokker-Planck-Kolmogorov equations.
    • Formulation of an event-triggered federated learning mechanism for algorithm convergence and communication efficiency.

    Main Results:

    • Derivation of an approximate optimal control policy and quantification of collective behavior probability density.
    • Guarantee of uniform ultimate boundedness for tracking errors and weight estimation errors using Lyapunov's direct method.
    • Validation of the FL-ADP scheme's effectiveness and rationality through simulations on massive multi-uncrewed aerial vehicle systems.

    Conclusions:

    • The proposed FL-ADP control scheme effectively solves the optimal consensus problem in massive multiagent systems.
    • The method balances communication resource consumption with algorithm convergence, outperforming existing approaches.
    • The developed technique provides a robust and efficient solution for real-time adaptive optimal consensus control in large-scale systems.