Tracking Control for the Connection Relationships of Discrete-time Complex Dynamical Network Associated with the Controlled Nodes

Abstract

In this paper, a general discrete-time complex dynamical network is regarded to be composed of the nodes subsystem and the links subsystem which are mutually coupled. Different from the existing researches on the stabilization and synchronization of nodes group, this paper mainly focuses on the dynamical behavior of connection relationships between the nodes, and the network nodes only play a helping and secondary role in the dynamics of connection relationships. Due to the state of the links subsystem is difficult to be measured accurately in practice appliances, the Riccati difference equation without any control input is employed as the dynamic model of the links subsystem, in which the dynamic coupling term is the first order polynomial about the state of nodes. With the helping of controlled nodes, the tracking problem is discussed for the links subsystem. By using the coupling algebraic relation between the reference tracking targets of the nodes subsystem and the given tracking target of the links subsystem, the tracking control scheme is proposed for the nodes subsystem to force the links subsystem converges asymptotically to the given target. Finally, the simulations are used to show the validity of the method in this paper.