Robust Synchronization And Control For Memristive Neural Networks

Memristor was originally proposed by professor Chua in 1971,and it was realized by Hewlett-Packard Laboratories using materials of TiO2.Memrostor was predicted as the fourth circuit element except the other three elements-resistor,capacitor and inductor.The type of neural networks are called memristor-based neural networks,if the synapse is made of memrostor.In this paper,we aim to investigate the robust synchronization problems of memristor-based neural networks.Owing that the MNNs belong to the swithing-jump system with the features of discontinuous right-hand sides,then the theories of differential inclusion and set-valued maps are employed.And with the framework of Filippov's sense,three problems of robust synchronization are analysed including asymptotic synchronization,exponential synchronization and adaptive synchronization.The main research contents and achievements are as follows.(1)In the light of the defect in the existing results that the drive and response MNNs were totally matched,the nonidentical characters such as unmatched coefficients and time-varying delay mismatch are considered.What's more,pinning method is used to control partial nodes to synchronize the all nodes to achieve asymptotic synchronization.And the stability sufficient conditions are given by Lyapunov function method.At last,the effectiveniss for the desinded control laws are verified by numerical simulation.(2)Considering the strong mismatch features such as mismatch of activation function,mismatch of switching-jump and mismatch of input current,the exponential synchronization is achieved by pinning controller in this chapter.And the parameter stable region for controller can be computed quantitatively,then the synchronization errors can enter the desired error bound within the given settle time.And a simulation is given to verify the feasibility of achieved results.Finally,an simulation example of secure communication is given,and it isverified that reliable secure communication can be achieved via synchronized IVfNNs.(3)Be aimed at the deficiency in the previous results that the MNNs models are simplified unreasonably,here we design decoupling strategy to separate the coupling relations between three coefficients,it makes the models are more accurate and reasonable.Furthermore,considering that the activation functiosn in the former articles were continuous,in this paper we extend the functions to discontinuous types.Thus,the models are more close to practice.And an adaptive controller is devised to achieve asymptotic synchronization.At last,the effectiveness is checked by numerical simulation.