Research On Some Problems Of Control Synchronization Of Complex Networks

Complex network is a new science derived from nonlinear science and can be regarded as an important branch of complexity science.Complex networks exist widely in the real world,such as Internet,mobile communication network,transport network,power network,economic and financial network,biological network,social network,etc.,without much exaggeration to say that we live in a world of network.Synchronization,as one of the most typical dynamic phenomena in complex networks,has become a research hotspot in recent years due to its wide applications in the fields of image encryption,information processing and public transportation.Although research on control synchronization of complex networks has gained many outstanding achievements,however,researchers often impose various restrictive conditions on the network model for the convenient of research,the actual complex network model is extremely complicated,and how to build a more realistic network model needs further exploration.On the other hand,for a determined network model,there are still many problems to be solved urgently in designing simple and efficient controllers to achieve the goal of network synchronization.In this paper,based on Lyapunov stability theory and some mathematical tools,several control synchronization problems of complex networks are studied by combining theoretical analysis with numerical simulation,the specific work is introduced as follows:(1)The control synchronization problems of two kinds of complex networks are studied based on adaptive control.The work can be concluded two aspects:?for the complex networks with time-varying inner and outer coupling matrices,the effects of controller parameters on network synchronization are studied by setting up linear feedback controllers and adaptive controllers respectively.Based on Lyapunov stability theory,a suitable positive definite function is constructed,and the sufficient conditions for synchronization of complex networks are given.?for the uncertain complex networks with time-varying node delays and multiple time-varying coupling delays,a simple linearization method is selected under the condition of norm boundedness.By adding adaptive controllers,the local synchronization and global synchronization criteria of complex networks are studied respectively.By virtue of the Lyapunov stability function theory and Cauchy matrix inequalities,synchronization criteria are proved in detail.(2)The control synchronization problems of two kinds of delayed complex networks are disscussed based on aperiodical intermittent control.The work can be concluded two aspects:?for the complex network with node delay and coupling delay,these two delays are non-equal and independent.Linear feedback control and adaptive control are combined with aperiodical intermittent pinning control respectively,and the capacity consumption is further reduced by pinning part of nodes in the network.Based on the Lyapunov stability theory,the synchronization protocols are strictly given.? for the delayed bipartite network with non-delay and delay couplings,the connecting edges between two sets of nodes can be directional and weighted.By constructing linear feedback aperiodical intermittent controllers,the Lyapunov stability theory,matrix decomposition property and other mathematical techniques,the sufficient conditions for synchronization of drive-response bipartite networks are obtained.(3)The robust control synchronization problems of two kinds of complex networks with disturbances are analyzed.The work can be concluded two aspects:?for the nonlinear complex network with parameter disturbances and mixed delays,the effects of nonlinear coupling,parameter disturbances,time-varying node delays,time-varying coupling delays and time-varying distributed delays are considered.The simple linear matrix controllers are designed and the control strategy is robust to parameter disturbance.Based on the Lyapunov stability theory and linear matrix inequalities,sufficient conditions for outer synchronization of complex networks are obtained.?for the two different dimensional nonlinear networks with parameter and external disturbances,a robust adaptive method is used to compensate the network disturbances.By designing adaptive hybrid controllers and a suitable dimensional scaling function matrix,the modified function projective lag synchronization between two networks is realized,and the correctness of the conclusion is proved based on the Lyapunov stability theory.(4)The finite-time control synchronization problems of tvwo kinds of complex-valued networks with delays are explored.The work can be concluded two aspects:?for a fully complex-valued network with coupling delays,by the complex-valed operation properties,the complex-valued network is decomposed into two equivalent real-valued networks.Suitable finite-time controllers are respectively designed to study the finite-time synchronization of complex networks with and without coupling delays.Based on Lyapunov stability theory,sufficient conditions for finite-time synchronization are given.? for the nonlinear complex-valued network with time-varying delays,the effects of nonlinear coupling,time-varying node delays and multiple time-varying coupling delays are considered.All variables and parameters are complex values.Based on Lyapunov function method and finite-time stability theory,the control synchronization criteria are strictly given,and the upper bound of time can be obtained by calculation.