Asymptotic outer synchronisation control for the complex dynamical networks based on the link observer

This paper utilises the synthesised link observers to investigate the asymptotic outer synchronisation for two complex dynamical networks (CDNs) with time-varying links, in which one is called as the drive network (DN), another is the response network (RN). Meanwhile, each CDN is regarded to be composed of two mutually coupled subsystems: the node subsystem (NS) and the link subsystem (LS). In each CDN, the dynamics of NS is modelled as the vector differential equation with the unknown interaction caused by the nodes state of another network, and the LS is modelled as the matrix differential equation with link output. Two kinds of differential equations are regarded to be coupled with each other due to the coupling relation between nodes and their connections. By employing the above dynamical models of NSs and the outputs of LSs, the asymptotic state observers of two LSs are constructed, respectively, by which the adaptive controller of NS is synthesised for the DN under some mild conditions. The results in this paper show that the synthesised adaptive controller ensures not only the asymptotic outer synchronisation is achieved for DN and RN but also the corresponding states of LSs are asymptotically the same. Compared with the existing literature, the most prominent highlight of this paper is that two link observers are synthesised under the unavailable links to assist the adaptive controller of NS in RN to achieve the asymptotic outer synchronisation. Finally, the effectiveness of the theoretical results in this paper is proved by the numerical simulation.