Fault-tolerant Synchronization Of Complex Dynamic Networks With Internal Coupling Faults

In recent years,with the rapid development of Internet and computer technology,people's daily life has also become digitized,informatized and networked.Human lives in the environment with a variety of dynamic complex network relations,the characteristics of complex networks exist in a wide range of physics,biology,communications and other fields.And the application of complex network is widely used in the real world,such as neural network,virus propagation network,smart grid,communication system,network security,social network,Internet and so on.As an important characteristic of dynamic complex network,network synchronization is the hot spot in the past ten years.Due to the complexity of the real complex network topology,many uncontrollable faults are occured on the system.The scale and damage are still increasing,which destroy the synchronization of complex dynamic networks.It is critical to find more effective measures to prevent and control malfunctions which ensure the system stability.Therefore,we must fully consider the actual situation,contact complex network characteristics,establish a reasonable dynamic complex network model,and apply different fault tolerant control strategies to achieve complex network synchronization for different network faults.This is of great significance to the practical application of dynamic complex networks.The main contents of this paper are as follows:Firstly,consider the network deviation occurs with inner-coupling faults.Analyze the synchronization capabilities of complex dynamic networks.The influence of dynamic complex network topology,coupling strength and inner-coupling on network synchronization capability is analyzed.By using Lyapunov stability theory and linear matrix inequality,the network topology,coupling strength and internal coupling are established to regulate the parameters of the network and achieve fault-tolerant synchronization of the complex networks.Secondly,for complex dynamic networks with network transmission delay and internal coupling deviation faults,external controller is applied to the network node to implement complex dynamic network fault tolerance synchronization.When the internal coupling error is unknown but bounded,based on the Lyapunov stability theory,the design criteria of the fault-tolerant controller are obtained,so that the complex dynamic network achieves synchronization in the event of internal coupling deviation faults and transmission delays.Thirdly,for networks with network transmission delays and internal coupling failures,there are cases of external noise interference or uncertain structures,and the problem of fault tolerance synchronization of complex dynamic networks is studied.Using pinning control theory,some nodes in the network are controlled to enables fault-tolerant synchronization of complex dynamic networks.Using Lyapunov stability theory,the design criteria of fault-tolerant synchronization controller are obtained to ensure the synchronization of complex dynamic network under the condition of the least controller.