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    Area of Science:

    • Robotics
    • Control Theory
    • Artificial Intelligence

    Background:

    • Formation control is crucial for multi-agent systems.
    • Heterogeneous, nonlinear, and uncertain agents pose significant control challenges.
    • Existing neural network (NN) designs often lack pre-defined layer structures.

    Purpose of the Study:

    • To address the formation control problem for heterogeneous, nonlinear, uncertain, second-order agents.
    • To present a tunable, three-layer NN capable of approximating unknown nonlinearities.
    • To ensure stability and semi-global asymptotic tracking in multi-agent systems.

    Main Methods:

    • A tunable three-layer neural network (NN) is designed for nonlinearity approximation.
    • Lyapunov theory is used to derive the NN weights tuning law.
    • A control strategy combining robust integral of the sign of the error feedback and NN-based control is employed.

    Main Results:

    • The proposed NN design allows pre-setting the number of neurons per layer.
    • The control strategy effectively compensates for unknown dynamics and disturbances.
    • Lyapunov stability theory proves the system's stability and semi-global asymptotic tracking.

    Conclusions:

    • The developed NN-based formation control method is effective and efficient for heterogeneous multi-agent systems.
    • The approach offers advantages in NN design by avoiding trial-and-error for layer configuration.
    • The rigorous stability analysis confirms the reliability of the proposed control strategy.