Synchronization Analysis And Application Of Complex Networks Based On Pinning Control

As we all know,most of the network systems develop towards the divergence trend under the natural condition without constraints.In the actual complex dynamic network,the nodes are generally described by nonlinear functions,and the coupling relationship between nodes can be divided into linear and nonlinear coupling,which makes the spatial structure of the network more complicated.In previous studies,most scholars only pay attention to whether the network achieves synchronization,ignoring the cost paid in the actual situation.In this paper,the idea of containment control is used to control some nodes in the network,which is conducive to reducing the cost of control.In addition,there are time delay,noise and other interference factors in the process of information transmission,which may cause the system to fail to reach the ideal state.Based on this,this paper uses the relevant knowledge of complex networks to establish the corresponding mathematical model to analyze the synchronization of the system.The main research work is as follows:1.The synchronization problem of a class of linearly coupled complex network systems is studied.It is assumed that the coupling relation of each node in the network is linear,and the external coupling matrix of the whole network does not require symmetry.Based on the control principle,by controlling some nodes of the coupled network,all nodes of the whole complex network system can reach the synchronization state.The Lyapunov function is constructed,the stability theory and inequality principle are used to analyze the system,and the appropriate restraining controller is designed.The sufficient conditions for the complex network to reach the synchronization state are obtained.In addition,in order to solve the problem of restraining the controller how to control the nodes to achieve the optimal,a loss function is introduced to determine the number of control nodes and feedback gain by finding the minimum value of the loss function,and the optimal combination is obtained.2.In this paper,the synchronization problem of a class of nonlinear coupled time-delay complex networks is studied,and the problem of how to make the network achieve exponential synchronization by holding the nodes in the nonlinear coupling state is discussed.Considering that there may be delay in the process of information transmission,delay signals are added to the network.The internal coupling matrix of complex network does not require symmetry,and the external coupling matrix without delay phase and with delay term does not require symmetry.By constructing Lyapunov function,using Razumikhin technique and inequality principle to analyze,a suitable restraining controller is designed,and a criterion for nonlinear coupled timedelay complex network to achieve synchronization is established.The validity of the theoretical derivation is verified by numerical examples.3.The complex network is applied to the UAV(unmanned aerial vehicle)network.Considering the uncertainties during flight,time delay and random noise are introduced in the model construction.The actual UAV network and the corresponding expected UAV network model are constructed,and the external synchronization characteristics of the network are analyzed.By designing an appropriate control controller to control a UAV,the actual UAV network and the corresponding expected UAV network can realize synchronization,that is,reach the preset position.By constructing Lyapunov function and using stability theorem,ITO formula and correlation lemma,sufficient conditions for the complex network to reach the synchronization state are obtained.Finally,it is assumed that each UAV is a Lorenz system,and simulation experiments are carried out to verify the validity of the theory.