Synchronization of Complex Dynamical Networks with Stochastic Links Dynamics

Abstract

The mean square synchronization problem of the complex dynamical network (CDN) with the stochastic link dynamics is investigated. In contrast to previous literature, the CDN considered in this paper can be viewed as consisting of two subsystems coupled to each other. One subsystem consists of all nodes, referred to as the nodes subsystem, and the other consists of all links, referred to as the network topology subsystem, where the weighted values can quantitatively reflect changes in the network’s topology. Based on the above understanding of CDN, two vector stochastic differential equations with Brownian motion are used to model the dynamic behaviors of nodes and links, respectively. The control strategy incorporates not only the controller in the nodes but also the coupling term in the links, through which the CDN is synchronized in the mean-square sense. Meanwhile, the dynamic stochastic signal is proposed in this paper, which is regarded as the auxiliary reference tracking target of links, such that the links can track the reference target asymptotically when synchronization occurs in nodes. This implies that the eventual topological structure of CDN is stochastic. Finally, a comparison simulation example confirms the superiority of the control strategy in this paper.

Differential Entropy-Based Fault-Detection Mechanism for Power-Constrained Networked Control Systems

“…The SNR limitations presented in [ 9 ], which are fundamental in nature, deal with unstable single-input–single-output (SISO) LTI plant models, characterizing the initial bound on the channel SNR required to achieve feedback-loop stability for a single-channel model in the closed loop. A mean square analysis to address the probabilistic nature of the communication network was also used, in a different context of synchronization, in [ 14 ]. An NCS extension of the setup proposed in [ 9 ] is presented in Figure 1 ; in this paper, we consider a memoryless additive white Gaussian noise (AWGN) communication channel for the communication network, which operates simultaneously over two paths: the direct path between the controller and the plant and the feedback path between the plant and the controller.…”