Synchronization And Optimal Control Of Complex Dynamical Networks

Network science was born thanks to the breakthrough of network theoretical models(small-world model and scale-free model),while investigating the effect of topology and node dynamics on synchronization is a challenging topic.Presently the studies of synchronization on complex networks has focused designing many types of controllers,e.g,pinning control,adaptive control and impulsive control,however most of them do not involve identifying unknown parameters and topological structures and optimal control of synchronization.In reality,identifying unknown information and optimal control of complex networks is helpful for designing robust networks,therefore this dissertation mainly studies synchronization of unknown networks and optimal control of synchronization,including proposing adaptive and pinning controllers to realize synchronization.Using optimal rules,we obtain a family of optimal controllers.In details,our works are as follows:In chapter 1,we introduce some basic knowledge of complex networks,including the development of complex networks and the method of realizing network synchronization,as well as the opportunities and challenges in complex network research.In chapter 2,we study the anti synchronization problem of two unknown coupled complex networks,the unknown information of the network is that node dynamics contains an unknown parameter vector.In the process of research,adaptive and pinning controllers are proposed,and then by using the theory of stability we get the theorem of anti synchronization of the network and the criterion of the number of the controlled nodes.The numerical results show that while the network reaches anti synchronization,the parameters of the network are accurately identifiedIn chapter 3,the topological identification of two unknown complex networks with perturbed terms is studied,and a controller for identifying networks' topology is proposed.With the help of the Lyapunov stability theory,we get the criterion for the network to achieve external synchronization.The numerical results verify the validity of the theory,when the network achieves external synchronization,the unknown parameters and topology of the network are accurately identified.It also shows that the disturbance term of the network has little effect on the synchronization of the network.In chapter 4,by using the Pontryagin minimum principle,the optimal synchronization of two networks is realized.When the balance between the control strength and the synchronization target is achieved,the optimal controller of the network is obtained.The numerical example shows that the synchronization error of the network is minimized under the limited time range based on the optimal controller.In chapter 5,we summarize the conclusions and give further studies.