Finite-time Synchronization Of Competitive Neural Networks With Time Delay Via Quantized Control

Recently,synchronization of neural networks has been widely applied in many fields including secure communication,image processing,model recognition and so on.Specially,competitive neural network is a kind of interesting neural networks,and its synchronization and control also have triggered many researchers' attention.Considering the practical application,synchronization of neural networks is usually required to be realized in a finite time.So,it is urgent and necessary to study the finite-time synchronization of competitive neural networks.On the other hand,in the evolution process,neural networks will inevitably be affected by some factors caused by environment.Those factors might have negative impacts on the synchronization of neural networks.Hence,this thesis studies finite-time synchronization of competitive neural networks under the influence of discontinuous activation function,time delay,impulsive effect and switching parameters.The main research works are as follows:In the chapter 2,finite-time synchronization of coupled competitive neural networks with proportional delay,discontinuous activation function and impulsive effect has been discussed.Since the proportional delay is time-varying and unbounded,discontinuous activations will induce uncertain Filippov solutions,and the impulse effects can cause sudden changes of state,the classical finite-time stability theory cannot be used directly.So,for overcoming these difficulties,new analytical techniques have to be developed.By constructing new Lyapunov functionals based on 1-norm and designing effective quantized control,several sufficient conditions are obtained without using the classical finite-time stability theory.Meanwhile,the settling time is explicitly estimated.Finally,numerical simulations are provided to illustrate the effectiveness of theoretical analysis.In the chapter 3,finite-time bipartite synchronization of switched competitive neural networks with time delay and signed graph has been considered.It is stressed that the cooperation relationship and competition relationship are coexist in the considered coupled network model.As for the synchronization of switched systems,the method of multiple Lyapunov function is usually adopted since it can produce less conservatism synchronization criteria compared with a common Lyapunov function.But,if the multiple Lyapunov function technique is used,the increment coefficient is often introduced at the switching instants,which induces difficulty in estimating settling time.In order to achieve the finite-time bipartite synchronization,an effective quantized controller and a novel multiple Lyapunov functional based on 1-norm are designed.Firstly,by combining the average dwell time,the effects of time delay and switching parameters are well solved.Note that the sufficient criteria formulated by linear programming is established and the settling time of the finite-time bipartite synchronization is estimated.Then,by re-designing multiple Lyapunov functional with the dwell time segmentation technique and convex combination method,the synchronization criteria and the estimation of the settling time of the considered system are obtained,and the restriction that the increment coefficient should be lager than one has been eliminated.Finally,the rationality of the two methods are verified by numerical simulations.Numerical simulation results show that the settling time obtained by the latter method is more accurate.