On Complex Network By Pinning Discontinuous Synchronization Control And Its Application

A complex network is a complex aggregate of some interlinked and interactive units with some characteristics and functions. Recently, complex networks have attracted a great deal of attention from many fields of science and engineering, such as control engineering, mathematics, computer science, biology and economy. Synchronization of complex networks is not only a common phenomenon within non-linear systems, but also a significant part for practical applications. In this dissertation, formation flying satellites with chaotic circuits are taken as a complex network. Based on the Lyapunov stability theory, the network is guaranteed to be synchronous by applying pinning discontinuous controller to a small fraction of its nodes, and some conclusions are applied to the chaotic secure communication of formation flying satellites.Firstly, the inner coupling matrix of complex network considered in other literatures is extended from unit matrix to symmetrical matrix, and pinning impulsive controllers are designed. The Lyapunov function is chosen for the error system, and the synchronization conditions are obtained. In addition, a BA scale-free network with 20 nodes is taken in simulation. The theoretical results derived here are proved to be effective. By analyzing the factors related to network synchronization, such as the coupling strength, the number of controlled nodes, and pinning schemes, some conclusions are given.Secondly, because there are transmission delays in the communication system of formation flying satellites due to the long transmission distance, computational limitation of hardware equipment, etc., which is considered to be the coupled delays in complex networks, the complex network with coupled delays is studied in this part. Pinning impulsive controllers are designed for a small fraction of the nodes, and delay independent criterions for the complex network synchronization are obtained. Simulation results show that the couple delay not only makes the complex network synchronization more difficult, but also brings fundamental changes in many characteristics of the complex network.Thirdly, pinning intermittent controllers are designed for the complex network with couple delay, and sufficient conditions of the complex network synchronization are obtained. The theoretical results derived here are proved to be effective in simulation, and a comparison between the pinning impulsive controller and the pinning intermittent controller is given. Then, the chaotic secure communication scheme of formation flying satellites is designed, and the sine wave and square wave is encrypted, respectively, to verify the secure communication effectiveness.Finally, the whole work of this dissertation is summarized, and some open fields are proposed for further research.