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    This study addresses discrete system consensus with bounded noise, proposing a novel algorithm (FCBN) that overcomes limitations of fixed-distribution noise models. FCBN ensures faster convergence and higher accuracy in practical applications.

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    Area of Science:

    • Control Systems Engineering
    • Distributed Computing
    • Network Science

    Background:

    • Existing consensus algorithms often assume noise with fixed distributions (e.g., Gaussian), which is unrealistic for many practical systems.
    • Bounded noise, prevalent in real-world applications, poses challenges to the convergence and accuracy of traditional consensus protocols.
    • Investigating consensus in discrete systems under bounded noise is crucial for robust distributed decision-making.

    Purpose of the Study:

    • To analyze the convergence properties of discrete systems under bounded noise.
    • To develop a novel consensus algorithm that effectively handles bounded noise and eliminates accumulative errors.
    • To demonstrate the superior performance of the proposed algorithm compared to existing methods.

    Main Methods:

    • Derivation of necessary and sufficient conditions for consensus convergence under bounded noise.
    • Development of an analytical bound for the state difference in general consensus algorithms.
    • Proposal and theoretical analysis of the Fast Consensus under Bounded Noise (FCBN) algorithm.

    Main Results:

    • Established conditions for consensus convergence in discrete systems with bounded noise.
    • Quantified the maximum state difference in general consensus algorithms under bounded noise.
    • FCBN algorithm demonstrated faster convergence and higher accuracy than general consensus algorithms in simulations.

    Conclusions:

    • Bounded noise significantly impacts consensus protocols, necessitating specialized algorithms.
    • The proposed FCBN algorithm offers a robust and efficient solution for achieving consensus in discrete systems with bounded noise.
    • FCBN enhances both the speed and precision of consensus, proving effective in extensive simulations.