Asymptotical outer synchronization control for the complex dynamical
networks with unknown bounded interaction via links dynamics
Abstract
The nodes and their connection relationships (CRs) are the two main
parts for a complex dynamical network (CDN). In existing theoretical
studies about the outer synchronization, the nodes are considered as the
main part of synchronization phenomena mainly associated by coupling
effect of CRs between nodes. However, if the CRs between nodes are
time-varying, they can also be regarded as one dynamic system coupled
with the nodes, and thus their state may evolve with time and maybe
assist the nodes to achieve the outer synchronization. From the angle of
large-scale systems, a CDN can be regarded as two interconnected
subsystems, one of which is the node subsystem (NS) and the other is the
link subsystem (LS). Hence, how the whole dynamic of LS contributes to
the outer synchronization of NS is one of worthy research problem. In
this paper, the two CDNs are considered with the unknown interaction. In
each CDN, the dynamics of NS is modelled as the vector differential
equation, the LS is modelled as the Riccati matrix differential
equation, and the two kinds of differential equations are coupled with
each other. By employing the above dynamic models of CDNs and the
synthesized coupling terms in the two LSs, the adaptive controller of NS
is synthesized for the response CDN. The results show that the outer
synchronization happens when the two LSs tracking the synthesized
auxiliary dynamic tracking targets. Finally, the numerical simulation is
given to show the effectiveness of the theoretical results in this
paper.