Research On Novel Methods Of Synchronization Control For Several Types Of Complex Dynamical Networks

As a hot spot of nonlinear science research,the study of complex networks has attracted the attention of a large number of scholars.It is found that the commonness and regularity of complex networks,the analysis of network synchronization performance and synchronization control are the main aspects for the complex networks researching.In order to meet the practical needs of engineering applications better and improve the existing theories of complex dynamical network,Taking the key problems such as the structure characteristics,synchronization control method and synchronization speed of complex dynamic networks into account,this dissertation analyses and discusses the synchronization problems of several kinds of complex dynamic networks.By synthesizing the practical factors of complex dynamical network,such as periodical time-varying topological structure,nodes with different dimensions,time-delay coupling,random disturbance,and so on.The synchronization algorithms are designed by means of adaptive feedback control,learning control and intermittent control,which promises the synchronization conclusions hold.Finally,some simulation examples are given basing on the theoretical analysis.The main research contents are as follows.1.The synchronization problem of complex dynamic networks with different dimensions of nodes and unknown control direction is studied with the help of the Nussbaum function.The corresponding adaptive controller is designed,and the sufficient conditions of synchronization of network are obtained according to the Lyapunov stability theory.In addition,based on the theory of finite-time stability and adaptive feedback control method,finite-time synchronization for a class of unknown time-delay coupled complex dynamical network with different dimensions of nodes is realized by a differential type of adaptive learning law designed for the coupling parameters and appropriate finite-time adaptive controllers,and the coupling structure is successfully estimated,and matrix projective synchronization of the controlled complex dynamical network is realized.The effectiveness and feasibility of the above two algorithms are verified by simulation examples.2.Based on the generalized inverse theory of full rank matrix and the fixed-time stability theory of differential equation,the scheme of fixed-time synchronization control is designed,and the appropriate composite energy function is selected for heterogeneous complex dynamical networks with different dimensions of nodes.Fixed-time matrix projective synchronization of heterogeneous complex dynamic networks with different dimensions of nodes is proved theoretically.Furthermore,the corresponding fixed-time matrix projection synchronization controlling method and sufficient condition are presented for such networks with uncertainties and time-varying delays.The simulation results shows that the control scheme is effective.3.The problem of exponential synchronization for a class of complex dynamic networks with unknown periodical coupling weights is studied.Combining with the Lyapunov-Krasovskii functional,the exponential synchronization conclusion of for the given network is proved by using the designed aperiodical intermittent control scheme.Moreover,basing on the finite-time stability theory of stochastic differential equations,the conditions for finite-time synchronization of complex dynamic networks with stochastic disturbances are obtained by using adaptive and nonlinear feedback control methods.Detailed theoretical derivation is given to verify the feasibility and effectiveness of the proposed design scheme.4.The concept of outer average synchronization among complex dynamical networks with different number of nodes is proposed.A suitable feedback control scheme and parameter adaptive update laws are designed.With the help of the persistent excitation condition,the parameters identification of nodes for the network is realized successfully.For the complex dynamical networks with time-varying delays and unknown information,the direction of control input is considered.The Nussbaum gain function is used to deal with the problem of control direction,and the adaptive controller and update laws of unknown information are designed.Combining with the persistent excitation conditions,sufficient conditions for asymptotical synchronization of network are obtained.The identifiability of unknown node parameters and outer coupling structure matrix in network system is proved.The numerical simulation results verify the accuracy of the proposed scheme.Finally,the main results of this dissertation is summed up.Furthermore,some existing problems and the future work were pointed out.