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    Area of Science:

    • Control Systems Engineering
    • Signal Processing
    • Networked Systems

    Background:

    • Silent packet loss (SPL) presents a significant challenge in state estimation, particularly in event-based systems.
    • Existing detection methods struggle with perfect accuracy, leading to complications in state probability distributions.
    • The interplay between event-triggered feedback and SPL complicates estimation in networked control systems.

    Purpose of the Study:

    • To propose a novel silent message-passing mechanism (SMPM) to mitigate the effects of SPL in measurement feedback channels.
    • To introduce a dynamic Chi-square ($d$-$\mathcal{X}^{2}$) detector with proven 100% detection accuracy convergence.
    • To design a state estimator for unstable systems incorporating SMPM and the $d$-$\mathcal{X}^{2}$ detector, establishing a stability condition.

    Main Methods:

    • Development of a silent message-passing mechanism (SMPM) compatible with event-based schedulers.
    • Introduction and theoretical validation of a dynamic Chi-square ($d$-$\mathcal{X}^{2}$) detector.
    • Design of a state estimator for unstable systems utilizing SMPM and the $d$-$\mathcal{X}^{2}$ detector.
    • Derivation of a stability condition linking SPL rate to estimation performance.

    Main Results:

    • The proposed SMPM effectively addresses SPL in measurement channels, even when coupled with event-based systems.
    • The $d$-$\mathcal {X}^{2}$ detector demonstrates convergence to 100% detection accuracy over time.
    • The developed estimator ensures stability for unstable systems under SPL conditions.
    • Simulations and experiments confirm the efficacy of the proposed methods.

    Conclusions:

    • The SMPM and $d$-$\mathcal {X}^{2}$ detector offer a robust solution for state estimation in the presence of silent packet loss.
    • The established stability condition provides crucial insights into system performance under varying SPL rates.
    • The findings are validated through comprehensive simulations and experimental studies, highlighting practical applicability.