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    This study introduces a novel two-stage method for distributed parametric consensus optimization problems (DPCOP). The approach enables distributed systems to reach consensus on shared parameters, enhancing efficiency in multiagent systems.

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    Area of Science:

    • Control Systems Engineering
    • Optimization Theory
    • Distributed Computing

    Background:

    • Traditional distributed optimization enforces identical states across agents.
    • Distributed Parametric Consensus Optimization (DPCOP) addresses systems with partially shared parameters.
    • DPCOP requires novel methods for distributed parameter agreement.

    Purpose of the Study:

    • To develop a two-stage optimization method for DPCOP.
    • To enable distributed consensus on parameters among agents.
    • To apply the method to distributed model predictive consensus problems.

    Main Methods:

    • A two-stage approach combining primal decomposition and distributed consensus.
    • Utilizing a distributed projected subgradient method for parameter consensus.
    • Solving local multiparametric problems to obtain subgradients.

    Main Results:

    • A discrete-time distributed algorithm with exponential convergence for specific DPCOPs.
    • Successful application to distributed model predictive consensus problems.
    • Demonstrated stability analysis for the proposed algorithm.

    Conclusions:

    • The proposed two-stage method effectively solves DPCOP.
    • The approach facilitates optimal output consensus in heterogeneous multiagent systems.
    • Case studies confirm the method's effectiveness in systems with high-order dynamics.