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    Area of Science:

    • Control Systems Engineering
    • Cyber-Physical Systems Security
    • Networked Systems

    Background:

    • Cyber-physical systems (CPSs) are increasingly vulnerable to sensor failures and false data injection (FDI) attacks.
    • Token bucket protocols (TBPs) introduce network-induced constraints on data transmission in CPSs.
    • Existing state estimation methods often struggle to address simultaneous TBP constraints, sensor failures, and FDI attacks.

    Purpose of the Study:

    • To develop a robust recursive state estimation algorithm for nonlinear CPSs.
    • To simultaneously address the challenges posed by TBPs, sensor failures, and FDI attacks.
    • To minimize the upper bound of the estimation error covariance.

    Main Methods:

    • Utilizing an intensive stochastic technique and the induction approach to derive the upper bound of the estimation error covariance.
    • Recursively computing estimator gains to minimize the derived upper bound.
    • Employing a stochastic model for random FDI attacks following a Bernoulli distribution.

    Main Results:

    • An effective recursive state estimation algorithm is proposed.
    • The algorithm demonstrates the capability to handle TBP constraints, sensor failures, and FDI attacks concurrently.
    • The upper bound of the estimation error covariance is successfully minimized.

    Conclusions:

    • The proposed state estimation scheme is effective in enhancing the security and reliability of nonlinear CPSs.
    • The method provides a robust solution for state estimation under challenging network conditions and adversarial attacks.
    • The presented example validates the practical applicability and performance of the developed estimation algorithm.