Asymptotical outer synchronization control of the complex dynamical networks via unknown interaction and links dynamics

Abstract

The nodes and links connecting them are the two main geometric elements of a complex network. If the nodes and links change over time, all the nodes and all the links are regarded the dynamic systems, respectively, and thus, a complex dynamical network (CDN) can be regarded to be composed of the two interconnected subsystems: the nodes subsystem (NS) and the links subsystem (LS). The outer synchronization happens in two CDNs, which means that the state error between the two NSs converges to zero. However, the dynamics of LS is ignored in the existing literature about the outer synchronization. In addition, the existing literature rarely consider the unknown interaction between two CDNs into the outer synchronization. In view of this, this paper investigates the outer synchronization of two CDNs with the unknown interaction. By using the dynamics of LSs and synthesizing the adaptive control scheme, the outer synchronization is asymptotically achieved. The results in this paper show that the outer synchronization happens when the two LSs can track, respectively, the synthesized auxiliary dynamic tracking targets. Finally, the numerical simulation is given to show the effectiveness of the theoretical results in this paper.