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    Area of Science:

    • Control Systems Engineering
    • Robotics
    • Networked Multiagent Systems

    Background:

    • Controlling nonlinear discrete-time multiagent systems with unknown dynamics and multi-input multi-output (MIMO) characteristics presents significant challenges.
    • Existing formation control methods often require precise knowledge of system dynamics, limiting their applicability.
    • Bipartite graph structures introduce complexities in coordination and control strategies.

    Purpose of the Study:

    • To develop a model-free adaptive control (MFAC) protocol for bipartite formation control in nonlinear discrete-time multiagent systems.
    • To address systems with completely unknown dynamics and multi-input multi-output (MIMO) configurations.
    • To ensure bounded-input bounded-output (BIBO) stability and asymptotic convergence of formation tracking errors.

    Main Methods:

    • Utilized compact-form dynamic linearization (CFDL) with a pseudo-Jacobian matrix (PJM) to model unknown nonlinear dynamics.
    • Designed a distance-based formation term leveraging structurally balanced signed graphs.
    • Developed a bipartite formation model-free adaptive control (MFAC) protocol using only measured input and output data.

    Main Results:

    • The proposed MFAC protocol achieves bounded-input bounded-output (BIBO) stability for the multiagent system.
    • Demonstrated asymptotic convergence of the formation tracking error, ensuring precise group coordination.
    • Validated the protocol's effectiveness through two numerical simulation examples.

    Conclusions:

    • The developed bipartite formation MFAC protocol effectively controls nonlinear discrete-time multiagent systems with unknown MIMO dynamics.
    • The approach offers a robust solution for formation control problems where system identification is infeasible.
    • The method provides a practical framework for achieving stable and accurate formations in complex multiagent scenarios.