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    Area of Science:

    • Control Systems Engineering
    • Network Security
    • Signal Processing

    Background:

    • Sensor networks are vulnerable to Byzantine attacks, compromising data integrity.
    • Time-varying state-saturated systems require robust filtering techniques.
    • Token Bucket Protocol (TBP) regulates data transmission with stochastic packet sizes.

    Purpose of the Study:

    • To investigate distributed filtering for state-saturated systems under Byzantine attacks.
    • To develop a robust filtering strategy using TBP to mitigate attacks.
    • To establish an upper bound for filtering error covariance (FEC) and optimize filter gains.

    Main Methods:

    • Formulation of a Byzantine attack model targeting measurement signals.
    • Utilization of TBP to manage data transmission based on token availability.
    • Minimization of the filtering error covariance (FEC) upper bound to compute filter gains.
    • Matrix-based theoretical analysis to ensure boundedness of filtering error dynamics.

    Main Results:

    • An effective method for constructing an upper bound of the filtering error covariance (FEC) was developed.
    • Suitable filter gains were computed by minimizing the derived FEC bound.
    • The boundedness of the filtering error dynamics was rigorously proven.
    • Numerical simulations confirmed the proposed algorithm's effectiveness.

    Conclusions:

    • The proposed distributed filtering algorithm effectively handles Byzantine attacks in sensor networks.
    • The TBP integration ensures reliable data transmission under varying network conditions.
    • The developed theoretical framework guarantees the robustness and stability of the filtering error dynamics.