Synchronization And State Estimation Of Complex-Valued Memristive Neural Networks

As an extension of real-valued neural networks(RVNNs),the states,activation functions and connection weights of complex-valued neural networks(CVNNs)are complex-valued.Therefore,CVNNs have more abundant and more intricate dynami-cal behaviors than RVNNs.And CVNNs are widely used in engineering optimization,symmetry detection,quantum devices,remote sensing,electromagnetic imaging and so on.Memristor,as a new type of two terminal passive device,can maintain the weights after power failure,and has the characteristics of small size,low energy consumption and automatic memory,which has a significant effect on the storing and processing of information.Memristor has great advantages in simulating synapses in artificial neural networks,as a synapse in neurons,it can realize the continuous updating of synaptic weights,and it can also build neural networks structure with relatively high degree of integration.Therefore,complex-valued memristive neural networks(CVMNNs)have high research value.In this thesis,the synchronization and state estimation of CVMNNs with time-varying delays are studied.The primary contents are as follows:In the first chapter,the background and research status of neural networks,mem-ristive neural networks and CVNNs are introduced,and the state estimation of neural networks is also introduced.The second chapter discusses the exponential synchronization of CVMNNs with time-varying delays.Firstly,this chapter uses the real decomposition method to divide the CVMNNs into two real-valued systems,and applies these two real-valued systems to study the synchronization problem.And these two real-valued systems are not isolated,but interrelated.Then,integrating the theory of differential inclusion with the defini-tion of Filippov solution,the interval parameter systems are established.Moreover,an innovative quantized intermittent controller is designed,which takes full advantage of the networks' transmission capacity and has a significant effect on reducing the con-trol costs.Then,sufficient conditions are obtained to guarantee the global exponential synchronization between the CVMNNs and its response system via applying quantized intermittent control and the Lyapunov function technique.Finally,an explanatory illus-tration is offered to certify the validity of the theoretical outcomes.In the third chapter,the state estimation of complex-valued delayed memristive neu-ral networks(CVDMNNs)is studied.Firstly,a suitable state estimator is designed to es-timate CVDMNNs.Then,according to the real and imaginary parts of CVDMNNs and its estimation system,they are divided into two real-valued systems,respectively.And the error state systems are established by using these real-valued systems.In addition,the sufficient conditions related to delay are given to guarantee the global asymptoti-cal stability of the error state systems by applying Lyapunov stability theory and linear matrix inequality technology.Finally,an explanatory instance is given to illustrate the correctness of the theoretical outcomes in this chapter.The fourth chapter makes a summary of the principal work of this thesis,and points out the shortcomings of the thesis and the direction of future research.