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Consensusability and Global Optimality of Discrete-Time Linear Multiagent Systems.

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    This study solves consensusability and global optimality for discrete-time multiagent systems (MAS) with unstable dynamics. It establishes conditions for consensusability and reveals relationships between system dynamics and control performance.

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    Area of Science:

    • Control Theory
    • Systems Engineering
    • Robotics

    Background:

    • Multiagent systems (MAS) with unstable dynamics present significant challenges in achieving consensus.
    • Existing frameworks often struggle to guarantee global optimality and consensusability simultaneously for such systems.

    Purpose of the Study:

    • To develop a unified framework for solving consensusability and global optimality problems in discrete-time linear MAS with unstable dynamics.
    • To establish necessary and sufficient conditions for consensusability and derive bounds for the consensus region.

    Main Methods:

    • Utilizing the maximal disc-guaranteed gain margin (GGM) of the discrete-time linear quadratic regulator (LQR).
    • Deriving bounds for the consensus region based on unstable eigenvalues.
    • Employing inverse optimal control to analyze global optimality conditions.

    Main Results:

    • Sufficient and necessary conditions for consensusability are established.
    • Two bounds of the consensus region are derived solely from unstable eigenvalues.
    • A relationship between maximal GGM and intrinsic entropy rate is revealed for single-input MAS.
    • Conditions for achieving globally optimal consensus are proven, with limitations vanishing for marginally stable MAS.

    Conclusions:

    • The proposed framework effectively addresses consensusability and global optimality for discrete-time linear MAS with unstable dynamics.
    • The findings provide critical insights into the relationship between system eigenvalues, control performance, and consensus achievement.
    • The study successfully solves the minimum-energy-distributed consensus control problem for marginally stable MAS.