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    Summary
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    This study introduces a new control method for nonlinear multi-agent systems (MASs) that ensures followers track a leader's output in a predefined time, even with constraints. This approach handles both cooperative and adversarial interactions for robust consensus tracking.

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    Area of Science:

    • Control Theory
    • Nonlinear Systems
    • Multi-Agent Systems (MASs)

    Background:

    • Achieving consensus tracking in nonlinear multi-agent systems is challenging due to state constraints and complex dynamics.
    • Existing finite-time and fixed-time control methods have limitations in achieving precise tracking within a specified timeframe under constraints.

    Purpose of the Study:

    • To develop a predefined-time bipartite consensus tracking control framework for nonlinear MASs with asymmetric full-state constraints.
    • To enable follower agents to track either the leader's output or its opposite within a user-defined time.
    • To address unknown nonlinearities and asymmetric state constraints effectively.

    Main Methods:

    • Utilizing an improved time-varying nonlinear transformed function to manage asymmetric full-state constraints.
    • Employing radial basis function neural networks (RBF NNs) to approximate unknown nonlinear functions.
    • Constructing predefined-time adaptive neural virtual control laws via backstepping and estimating derivatives using first-order sliding-mode differentiators.

    Main Results:

    • The proposed control algorithm guarantees bipartite consensus tracking performance for nonlinear MASs within a predefined time.
    • The boundedness of all closed-loop signals is maintained, ensuring system stability.
    • Simulation results on a practical example validate the effectiveness of the developed control strategy.

    Conclusions:

    • The presented framework successfully achieves predefined-time bipartite consensus tracking for nonlinear MASs under asymmetric full-state constraints.
    • The integration of nonlinear transformation, RBF NNs, and adaptive control provides a robust solution for complex MAS problems.
    • This method offers enhanced control over tracking objectives and system stability within a guaranteed time.