Research On Synchronization Analysis And Control Strategy Of Complex Networks

Complex network is a large-scale network with complex topological structure and dynamic behavior,which exists widely in nature and society and has numerous types.The research of the complex network is an important branch of complexity science,and it is a comprehensive research topic that crosses the fields of mathematics,statistical physics and computer science.The intersection and integration of disciplines makes the research of complex network-related topics wider and scientific meaning stronger.Complex network synchronization is one of a typical dynamic behavior of engineering application demand.And the exploration and analysis of the complex network synchronization control law is an important direction of the complex network research.The related research achievements have been widely used in information transmission,electronic circuit,robot lined up,and other fields,which become the focus in the study of theory and application.In this paper,modern control theory combined with complex network theory,Lyapunov stability theory and other theories are used to study the complex network synchronization control problem with multiple complex factors.Some network synchronization control strategies based on adaptive control,coupling control and sliding mode control are given.The main contents include:1.For the research on the projection synchronization control of uncertain complex networks,the existing methods generally simplify the network model and weaken the problems of possible conditional factors.A drive-response network model that considers unknown parameter,coupling delay,different node and topology and other factors is constructed.And a novel bidrectional coupling synchronous control strategy is proposed,which utilizes the coupling relationship between networks to overcome the influence of multiple uncertain factors and constraints,then realizes the asymptotic projection synchronization between complex networks and estimate the unknown parameters simultaneously.Moreover,we consider the importance of ensuring the safe transmission of information within a limited time.On the basis of asymptotic projection synchronization,the finite-time projection synchronization and the finite-time lag-projection synchronization are discussed respectively.The effective adaptive controllers and updating rules of unknown parameters are obtained by using the finite-time stability theory and linear matrix inequality transformation.Finally,the feasibility and effectiveness of the proposed method are verified by simulation experiments.2.For the problem of the bidirectional coupling method requests external coupling effect for on both networks,the high cost of synchronization control and the low speed of synchronization,a unilateral coupling method is proposed.That synchronous control method can be accomplished aychronization by simply extracting the unilateral state variable signal from the response network and coupling it to the drive network.Firstly,considering that there are different node systems in the one network,and the response network contains unknown parameters and unknown topology structure.Then,a unilateral coupling synchronization control strategy is proposed.Synchronization is judged by Lyapunov stability theory and synchronization control criteria are given.The finite-time synchronization and the identification of unknown parameters and unknown topological structure are realized.Furthermore,considering that there are different node systems both within one network and between networks,the drive-response network is affected by unknown parameters and uncertain topology.Similarly,based on the idea of unilateral coupling control,according to the preset conditions,a synchronization control scheme is proposed to realize the identification of unknown parameters and the adaptive estimation of uncertain topological structure.In the simulation experiment,the correctness of the proposed method is verified at first.A comparison experiment is added to illustrate that the proposed unilateral coupling control strategy can reduce the number of coupling while ensuring a good synchronization performance.3.The sliding mode control method is applied to the finite-time synchronization control of multiple complex networks.Because the existing work is mainly focused on one or two networks,the proposed synchronization control method is difficult to be extended for synchronization control among multiple networks.In view of this situation,the synchronization control objects are extended to four and multiple networks by using the combination synchronization idea and sliding mode control theory,and a more universal synchronization control strategy is proposed to realize the finite time combination synchronization control among multiple complex networks.Firstly,for the finite-time synchronization of the four uncertain complex networks,which are combined as the form of A+B+C-D,a new sliding mode surface and sliding mode controller are designed,and the synchronization criteria for the finite-time combination synchronization of the four networks are obtained.Simulation experiments verify the correctness of the proposed method and reveal the influence of the value of key parameter on the synchronization rate.In order to overcome the disadvantages that the proposed control strategy only targets at a single fixed-number network,the synchronization problem of fixed-number network is further extended to that of multi-networks.The appropriate control input and unknown parameters updating rules are designed based on the sliding mode control method.Primarily,synchronization within a single subnetwork is realized.Then,the key nodes in the subnetworks are selected as the interaction center,and the key nodes of each subnetwork are under the synchronization control to achieve synchronization between multiple subnetworks.The proposed method only needs to add controllers to a node or a network to realize synchronization controller,which can effectively reduce the cost of synchronization control.