Generalized Outer Synchronization Control For Complex Dynamic Networks With Different-dimensional Nodes

The complex dynamic network,as a mathematical graph theory model of complex dynamic system,consists of a numerous of dynamic nodes and links（connection relationship）,which can describe engineering networks such as the Internet,power networks,communication networks,as well as social networks such as social relationship networks and scientific cooperation networks.Outer synchronization is an important dynamical behavior that occurs among multiple complex dynamic networks,which reflects some consistency between corresponding nodes in different networks and widely exists in engineering,natural and social networks.Therefore,it is of great theoretical and practical significance to study the outer synchronization of complex dynamic networks.However,in most of the existing literature,the authors only focus on the case of the nodes in a complex network have the same state dimension.It is worth noting that the realistic networks with different-dimensional nodes exist also widely,but they didn’t give sufficient attention to the outer synchronization control of such networks.Therefore,in this thesis,we synthesize the generalized outer synchronization controllers for a class of complex dynamic networks with different-dimensional nodes,focusing on some similarity of the node dynamic behaviors and the dynamics of connection relationships with the network,respectively.The relevant studies are as follows.（1）A class of drive-response networks with different state-dimensional nodes and nonlinear coupling terms is considered,where the nodes in the same network have different dimension,and the corresponding nodes in two networks have similar dynamic behaviors.Under the situation that the network connection relationship is unknown constant,by using the similarity structure,the adaptive controller is synthesized to effectively achieve the generalized asymptotic outer synchronization between the two networks based on Lyapunov stability theory.（2）A class of nonlinear coupled time-varying drive-response networks with uncertainty is considered,where the corresponding nodes in two networks have different state dimensions.In the case that the connection relationship of the drive network is unavailable and the inner coupling term is bounded,by using the similar structure between the corresponding nodes of the two networks,the connection relations and adaptive controller are synthesized for the response networks based on Lyapunov stability theory and matrix analysis methods.Finally,the generalized asymptotic outer synchronization between two networks were achieved.The results show that the outer synchronization controller can be simplified by using the dynamic similarity of the nodes and the dynamic of the connection relationship.What’s more,the obtained results expand the applicability of the network model to a certain extent.