The Synchronization Of Complex Networks And Its Application Based On Pinning Control

Synchronization is one significant dynamic behavior of various natural and artificial complexnetworks. Now it plays an important role in the communication systems, sensor networks and otherareas. Pinning control method only needs to control a small part of the nodes in a network, and it issimple, practical and economic, which has attracted wide attention from scientific researchers inrecent years. This paper mainly uses the pinning control method and the Lyapunov stability theory,and does some research on the synchronization of complex dynamical networks. The main researchachievements are as follows:Firstly, there are always various kinds of interference factors in the real networks, which maybeaffect the synchronization performance of the networks. So the synchronous behavior of complexdynamical networks under the external interference via pinning control is investigated in this paper.Several pinning synchronization criteria are proposed to ensure synchronization of the wholenetwork with a guaranteedH performance index, and the controlled network has a certaininterference rejection capability.Secondly, how many nodes should be pinned to achieve synchronization of a network? Solvingthis problem has some practical meanings. Based on pinning and adaptive control method, thispaper designs state-feedback controllers, and coefficients of the adaptive law are given, which aresimply as constants in the past researches. Sufficient condition under given conditions is deduced toreach synchronization of state-coupling complex networks, and pinned number of a network withfix topology and coupling strength can be calculated theoretically.Thirdly, in some real networks, some nodes’ states may be unknown or difficult to measuredirectly, so this paper designs output-feedback adaptive pinning controllers, which are more suitableto the practical engineering applications, and coefficients of the adaptive law are related to thecontrolled nodes of the network. Under the effects of output-feedback adaptive pinning controllers,the synchronization problems of state-coupling and output-coupling networks are respectivelystudied, and synchronization conditions are obtained by pinning control. The conclusions can beused to easily estimate the minimum number of pinned nodes.Fourthly, in some actual networks, the coupling between the nodes maybe nonlinear, andinternal states of these networks maybe also unknown, so this paper studies the synchronizationproblem of nonlinear-coupling complex dynamical networks. The output-feedback adaptive controllers are constructed through the output variable of only part of nodes, and coefficients of theadaptive law are given. Synchronization criterion is derived to realize synchronization ofnonlinear-coupling networks. The method proposed in this paper can calculate the number ofpinned nodes of nonlinear-coupling networks, which has a certain application value.Finally, pinning control method of complex networks is applied to sensor networks. Consideringsome uncertain factors, such as the obstacles in the practical environment, network fault and so on,some sensors may be difficult to measure all the states of the target at some moments. Based on theabove theoretical research, this paper designs adaptive pinning controllers, and the target’s states areestimated by only a small fraction of sensors’ nodes. The method can reduce energy consumption ofsensors, and has a practical engineering significance. The numerical simulation results show that theestimations of all sensors on the target will be eventually consensus under given conditions.