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Consensus in continuous-time multiagent systems under discontinuous nonlinear protocols.

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    This study analyzes nonlinear discontinuous consensus protocols for multiagent systems. We establish conditions for achieving consensus in fixed and switching network topologies, enabling predictable multiagent coordination.

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    Area of Science:

    • Control Theory
    • Network Science
    • Distributed Systems

    Background:

    • Consensus protocols are crucial for multiagent systems coordination.
    • Analyzing nonlinear discontinuous protocols over directed graphs presents significant challenges.
    • Understanding network topology dynamics (fixed vs. switching) is key for robust consensus.

    Purpose of the Study:

    • To provide a theoretical analysis of nonlinear discontinuous consensus protocols for multiagent systems.
    • To investigate consensus conditions under both fixed and randomly switching network topologies.
    • To develop conditions ensuring asymptotic consensus and almost sure consensus.

    Main Methods:

    • Integration of nonsmooth stability analysis and graph theory.
    • Development of sufficient and necessary conditions for fixed topologies.
    • Formulation of sufficient conditions for randomly switching topologies, including i.i.d. switching sequences.

    Main Results:

    • A necessary and sufficient condition for asymptotic consensus in fixed topology networks is derived, with explicit consensus value calculation.
    • A sufficient condition for achieving consensus almost surely in switching topology networks is established.
    • The generalized blinking model demonstrates practical applicability of the proposed protocols.

    Conclusions:

    • The theoretical framework effectively addresses nonlinear discontinuous consensus in complex multiagent networks.
    • The findings provide a robust foundation for designing and analyzing distributed consensus algorithms.
    • The research contributes to advancing the understanding of coordinated behavior in dynamic multiagent systems.