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    Area of Science:

    • Control Theory
    • Multiagent Systems
    • Robotics

    Background:

    • Existing research often relies on centralized protocols or specific algebraic Riccati equation-based designs.
    • Optimal leader-following consensus in multiagent systems with pre-given cost functions and topologies presents unique challenges.
    • Distributed protocols, dependent only on relative states, are desirable for practical implementation.

    Purpose of the Study:

    • To develop a novel distributed optimal protocol for leader-following consensus in single-integrator multiagent systems.
    • To address the limitations of existing methods by handling pre-given global cost functions and topology structures.
    • To derive an explicit formula for the cost function and identify optimal gain parameters for distributed control.

    Main Methods:

    • A novel design strategy for distributed optimal protocols over directed tree topologies.
    • Explicit derivation of the consensus error dynamics.
    • Development of an online-implementable algorithm for cost function parameterization and derivation of an explicit formula for gain parameters.

    Main Results:

    • Rigorous proof for the existence of optimal gain parameters, confirming the feasibility of the distributed optimal protocol.
    • Derivation of an explicit formula for the cost function concerning all agents' gain parameters.
    • Minimization of the explicit formula to determine the optimal gain parameters.

    Conclusions:

    • The proposed novel design strategy successfully enables a distributed optimal leader-following consensus protocol for multiagent systems.
    • The derived explicit formula and optimization method provide a clear pathway to achieving optimal consensus gains.
    • Simulation examples validate the effectiveness of the theoretical results in practical scenarios.