Some theoretical results of synchronization of a linearly coupled dynamical system with random perturbation on a network

Abstract

This paper attempts to investigate synchronization of a coupled dynamical system with random noise on a network (graph). Some mathematical results are obtained in this paper, first, a synchronized threshold is given for a linearly coupled dynamical system perturbed by the random noise; second, when the linearly coupled dynamical system with random noise reaches synchronization, the long time behavior of identical orbit on each node is discussed; finally, some interesting comparison between the synchronization of the coupled gradient system and its small random perturbed system is considered.

Leader-following Consensus Problems with a Time-varying Leader under Measurement Noises

“…Let x * = x − x 0 1 and v * = v − v 0 1. We then obtain an error dynamics of (10) as follows: dε(t) = F (t)ε(t)dt + G(t)dW (t), t ≥ 0 (11) where…”

“…In recent years, there has been an increasing research interest in the distributed coordination for multi-agent systems. This is partly due to its broad applications in many areas such as cooperative control of unmanned aerial vehicles, formation control [1,26,27] and swarming behaviors of social living beings [11,16,30].…”