Consensus Under Bounded Noise in Discrete Network Systems: An Algorithm With Fast Convergence and High Accuracy

Most existing works investigate consensus with noise following a certain distribution, e.g., Gaussian distribution, with fixed expectation and variance, which may not be satisfied in practical applications. This paper investigates the discrete system consensus under bounded noise, which is important and practical problem. We first provide necessary and sufficient conditions for the convergence of consensus under bounded noise. To be more general, we derive an analytical bound to show the max-min difference between the nodes' states when the general consensus algorithm converges to a stable state. Then, a novel consensus algorithm, fast consensus under bounded noise (FCBN), is proposed to eliminate the accumulative error caused by the bounded noise. It is proved that FCBN has a faster convergence speed and a higher consensus accuracy than general consensus algorithms. Extensive simulations demonstrate the effectiveness of the proposed algorithm.