Research On The Synchronization And Control Of Several Complex Networks With Time Delays

Nowadays,with the development of computer and information technology,the hu-man society has entered a new time of network.From the Internet to WWW,from the power network to transportation network,from the biological of the brain neural network to metabolic network,from the scientific research cooperation network to political,eco-nomic,social networks,etc.,humans have been living in a world,which is constituted by all kinds of CNs.This phenomenon has changed people's traditional view of the real network,and the research on CNs has also entered into a new area.Recently,CNs have become a hot topic in different scientific fields(including engineering,physics,biology,mathematics,chemistry,etc.).Due to CNs have many broad applications in various ar-eas such as signal processing,multi-agent consensus,pattern recognition,wireless sensor network,secure communication and robotics control,so it is very important for us to study the problem of synchronization and control for CNs in both theory and practices.This thesis deals with the issue of synchronization and control for CNs with time delays,for example time-varying delays CNs,stochastic CNs with time-varying delays,T-S fuzzy CNs,etc.Based on the Lyapunov stability theory and mathematical analy-sis methods,by resorting to some continuous control approaches,such as linear feedback control,pinning control;discrete control methods,including sampled data control,impul-sive control;hybrid control method,such as pining impulsive control;the synchronization problem of CNs has been studied.Moreover,some conditions on the synchronization of network are provided,such as complete synchronization,outer synchronization and lag synchronization.In the end,the effectiveness and superiority of the proposed method is illustrated by the MATLAB numerical simulation examples.The main research works of this thesis are summarized as follows:1.The lag synchronization issue of CNs with unknown signal propagation delays is investigated.Since the time delay is unknown,it usually leads to instability,even network performance is reduced.Meanwhile,this makes it difficult to use existing methods for processing.To this end,by designing new feedback controllers and effective Lyapunov functional,and with the aid of estimated unknown signal propagation delay which is related to the setting time,the CNs with unknown signal propagation delays can achieve finite-time lag synchronization.2.The problem of lag synchronization for CNs with multiple time delays(Discrete time-delays,Distributed time delays)is studied.Based on the Lyapunov stability theory and mathematical analysis technology,by constructing an useful Lyapunov functional and designing a pinning feedback controller,the lag synchronization of the network is achieved.Moreover,the relationship among the number of pinned nodes and network nodes dynamics,coupling matrices,and the designed parameter matrices is analyzed.3.The synchronization for a class of CNs with communication delays is addressed.Due to the digital control based on the computer takes merits in speed,accuracy,and low cost during the control process,this thesis proposes an aperiodic memory sampled-data feedback control protocol.By resorting to an improved Lyapunov functional,the con-cerned CNs model can achieve synchronization.Moreover,considering that the system is disturbed by noise,_?synchronization can make the influence of noise interference on synchronization error smaller than expected,this thesis further studies the_?syn-chronization problem of CNs.4.The synchronization issue of general CNs via pinning impulsive control is in-vestigated.By combining with the pinning control and impulsive control and choosing the pinned nodes based on the synchronization error norms at different impulsive in-stants.Then,under an effective Lyapunov functional,the synchronization of concerned networks can be achieved.Moreover,the various possible cases between the delays size and impulsive intervals are also discussed.5.The synchronization issue of the delayed SCNs is addressed.We not only takes the random noise and temperature into consideration in the model,but also further con-siders the delayed effects in the controller.With the help of effective Lyapunov functional and a mathematical induction approach,by designing a delayed impulsive protocol based on the pinning control,the proposed SCNs model can achieve synchronization.6.The problem of synchronization for a class of delayed CNs with partial coupling and T-S fuzzy model is studied.With the aid of a decoupling scheme,by constructing a modified time-dependent Lyapunov functional and designing a memory sampled-data control approach,new criteria are developed to guarantee the synchronization of con-cerned networks.