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    This study designs time-varying deployment for nonlinear multiagent systems (MASs) within a set time. The novel approach transforms MAS deployment into stabilizing discrete-space partial differential equations (PDEs), ensuring timely system configuration.

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    Area of Science:

    • Control Theory
    • Robotics
    • Networked Systems

    Background:

    • Multiagent systems (MASs) require coordinated deployment strategies.
    • Existing methods often struggle with prescribed-time convergence for nonlinear systems.
    • Real-world agent distributions are inherently discrete.

    Purpose of the Study:

    • To design prescribed-time time-varying deployment schemes for first-order and second-order nonlinear MASs.
    • To develop controllers based on discrete-space partial differential equations (PDEs).
    • To ensure deployment completion within a user-defined timeframe.

    Main Methods:

    • Formulating deployment as stabilization of discrete-space PDE systems.
    • Utilizing information on relative and absolute positions/velocities via a communication network.
    • Introducing static-feedback controllers based on spatial variables.
    • Applying Dirichlet and Neumann boundary conditions using virtual agents.

    Main Results:

    • Derived algebraic inequality criteria for guaranteed prescribed-time convergence.
    • Successfully transformed MAS deployment into discrete-space PDE stabilization.
    • Demonstrated effectiveness through two numerical examples.
    • Addressed limitations of continuous-space PDE models for discrete agent distributions.

    Conclusions:

    • The proposed discrete-space PDE approach effectively achieves prescribed-time deployment for nonlinear MASs.
    • The method offers a novel perspective compared to existing continuous-space PDE techniques.
    • The findings are validated by numerical simulations, confirming practical applicability.