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Partial-Nodes-Based State Estimation for Complex Networks With Unbounded Distributed Delays.

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    This study introduces partial-nodes-based (PNB) state estimation for complex networks with delays and noise. The PNB method estimates network states using only a fraction of nodes, ensuring bounded estimation errors.

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    Area of Science:

    • Control Systems Engineering
    • Network Science
    • Signal Processing

    Background:

    • Complex networks are crucial in various fields, but state estimation faces challenges like distributed delays and measurement noise.
    • Traditional state estimation requires data from all nodes, which is often impractical or computationally intensive.

    Purpose of the Study:

    • To develop a novel partial-nodes-based (PNB) state estimation method for complex networks.
    • To address challenges posed by unbounded distributed delays and energy-bounded measurement noises.
    • To ensure exponential ultimate boundedness of estimation error dynamics.

    Main Methods:

    • Designing a PNB state estimator that utilizes measurement outputs from a fraction of network nodes.
    • Establishing sufficient conditions for the existence of PNB state estimators.
    • Characterizing the explicit expressions for the gain matrices of these estimators.

    Main Results:

    • The PNB state estimator guarantees that the error dynamics of network state estimation are exponentially ultimately bounded, even with measurement errors.
    • Sufficient conditions for the existence of PNB state estimators were derived.
    • When network measurements are noise-free, the results simplify to exponential stability of the error dynamics.

    Conclusions:

    • The proposed PNB state estimation method is effective for complex networks with delays and noise.
    • The method offers a practical solution when full network observability is not feasible.
    • Numerical examples validate the theoretical findings and the efficacy of the PNB approach.