| In recent years,neural networks(NNs)has gained broad interest in many fields,includ-ing mathematics,artificial intelligence,optimized decision,aeronautics and astronautics,and control science,etc.The establishment of NNs models can give basis for analyzing,judging and predicting the dynamic characteristics of the network.So far,there have many litera-tures about NNs synchronization control.However,due to the widespread existence of time delay will have a big effect on the steadiness of the system,so there are still many problems that need to be deeply explored,especially the influence of time delay on NNs.In this thesis,by means of ordinary differential equation,Lyapunov stability and matrix theoretical knowledge,the synchronization control of two classes of coupled NNs with time delays are studied.The main content is summarized as the following two points:1.Based on impulse time delay differential inequality,Lyapunov theory and the concept of average impulse interval,the quasi-synchronization of NNs with distributed and propor-tional delays is discussed.An impulsive controller is designed and some quasi-synchronization criteria of heterogeneous NNs with time delays are obtained.In addition,the theoretical error bounds of quasi-synchronization are estimated by using the parametric transformation formulas of distributed and proportional delays.In the end,listing two examples to prove the validity of the results.2.Cluster synchronization of NNs is studied under the pinning impulsive control.The nonlinear coupled NNs with time varying delay,under the condition that the coupling matrix is not symmetric or irreducible,a pinning impulsive controller is designed.The controller only part of the nodes are controlled at each impulsive instant.By constructing Lyapunov function and combining with LMI technology,the sufficient conditions for cluster synchro-nization are deduced.Finally,listing an example to prove the validity of the results. |
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