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    This study explores consensus in hybrid multiagent systems (MASs) using game theory. New protocols ensure system-wide agreement in both first-order and second-order hybrid MASs, verified by simulations.

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    Area of Science:

    • Control Theory
    • Artificial Intelligence
    • Network Science

    Background:

    • Multiagent systems (MASs) are crucial for distributed decision-making.
    • Achieving consensus (agreement) in MASs is a fundamental challenge.
    • Hybrid MASs combine different agent dynamics, adding complexity.

    Purpose of the Study:

    • To investigate consensus conditions for first-order and second-order hybrid MASs.
    • To develop and analyze novel consensus protocols for these systems.
    • To establish theoretical guarantees for achieving consensus.

    Main Methods:

    • Game modeling to define agent states based on Nash equilibrium.
    • Development of two distinct consensus protocols for each system order.
    • Application of graph theory and matrix theory for analysis.
    • Numerical simulations to validate theoretical findings.

    Main Results:

    • Sufficient and necessary conditions for consensus were derived for first-order hybrid MASs.
    • Sufficient and necessary conditions for consensus were derived for second-order hybrid MASs.
    • The proposed protocols were shown to be effective in achieving consensus.

    Conclusions:

    • Consensus in hybrid MASs can be achieved through game-based state selection and appropriate dynamics.
    • The theoretical conditions and protocols provide a framework for designing reliable distributed systems.
    • Numerical simulations confirm the practical applicability of the developed methods.