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    This study introduces distributed model predictive control (MPC) algorithms to solve the optimal consensus problem for multiagent systems. The proposed method ensures system stability and demonstrates efficiency in multirobot rendezvous control.

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    Area of Science:

    • Control Theory
    • Robotics
    • Distributed Systems

    Background:

    • Multiagent systems require coordinated behavior for tasks like rendezvous.
    • Asynchronous sampling presents challenges in achieving consensus in these systems.
    • Model Predictive Control (MPC) offers a framework for optimizing control sequences.

    Purpose of the Study:

    • To develop distributed MPC algorithms for solving the optimal consensus problem in asynchronous sampling single-integrator and double-integrator multiagent systems.
    • To ensure closed-loop system stability under specific agent weighting and sampling conditions.
    • To validate the proposed algorithm's efficiency through numerical simulations.

    Main Methods:

    • Distributed Model Predictive Control (MPC) is employed to minimize finite-time linear-quadratic performance.
    • Consensus state optimization is integrated within the control input calculation.
    • MPC is extended from a finite predictive horizon to an infinite horizon.
    • Stability conditions are derived based on agent weighting scalars and sampling steps.

    Main Results:

    • The proposed distributed MPC algorithms effectively solve the optimal consensus problem for asynchronous multiagent systems.
    • Finite-time performance is minimized distributively within each predictive horizon.
    • Conditions for guaranteeing closed-loop system stability were successfully derived.
    • Numerical examples confirmed the algorithm's efficiency in multirobot rendezvous scenarios.

    Conclusions:

    • The developed distributed MPC approach provides a robust solution for optimal consensus in asynchronous multiagent systems.
    • The derived stability conditions offer practical guidelines for system design.
    • The algorithm shows significant promise for applications in coordinated robotics and distributed control.