Synchronization Control Of Memristor-Based Neural Networks With Continuous Or Discontinuous Activations Functions

Artificial neural network(ANN) is a kind of computational structure developed on the basis of neurobiological research to model and simulate the the certain characteristics of the human brain including information processing, learning, associative memory,etc. Though, the current digital computers have the ability to computing the speed and complexity to emulate the brain functionality of animals like a spider, mouse, and cat,but ANN still can not effectively adjust and memorize the synapses among the neurons just like the human brain can. This is because the synapses among neurons in biological neural networks are known as long-term memories, but the conventional resistors cannot implement the function of memory. Thus, efficient circuit implementation of synapses is very important to build a brain-like machine.As the fourth basic circuit element along with the resistor, capacitor and inductor,memristor has very good characteristics such as nanoscale physical dimensions, low power consumption, excellent storage capacity, high durability, which make it as a powerful tool to realize artificial brain. In this thesis, we construct some memristor-based neural network(MBNNs) models by combining the information storage features of memristor to the high-speed parallel processing capability of neural networks. Based on the Filippov’s theory of differential equations with discontinuous right-hand side, by using Lyapunov functional method and nonsmooth analysis approach we will give some simple and novel conditions to ensure the synchronization of constructed networks. Finally, we give some numerical experiments with their numerical simulations to demonstrate the effectiveness and feasibility of the developed theoretical results.The main contributions and originality contained of this dissertation can be summarized as follows:The first chapter reviews the history and development MBNNs and introduces the research content of this paperThe second chapter deals with the problem of function projective synchronization for a class of memristor-based Cohen–Grossberg neural networks(MBCGNNs) with timevarying delays. Based on the theory of differential equations with discontinuous right-hand side, some novel criteria are obtained to realize the function projective synchronization of addressed networks by combining open loop control and linear feedback control. As some special cases, several control strategies are given to ensure the realization of complete synchronization, anti-synchronization and the stabilization of the considered MBCGNN.Finally, a numerical example and its simulations are provided to demonstrate the effectiveness of the obtained results.The third chapter investigates the exponential lag synchronization for a class of MBNNs with mixed time-delays via hybrid switching control method. Based on the theory of differential equations with discontinuous right-hand side, several new sufficient conditions ensuring the exponential lag synchronization of MBNNs are obtained by designing two different hybrid switching controllers and constructing novel Lyapunov functionals. Finally, a numerical example with simulation is given to show the effectiveness and feasibility of the obtained results.In the forth chapter, the finite-time synchronization is considered for a class of MBNNs with time-varying delays. Based on the theory of differential equations with discontinuous right-hand side, several new sufficient conditions ensuring the finite-time synchronization of MBNNs are obtained by using analysis technique, finite time stability theorem and adding a suitable feedback controller. Besides, the upper bounds of the settling time of synchronization are estimated. Finally, a numerical example is given to show the effectiveness and feasibility of the obtained results.The fifth chapter investigates the exponential synchronization of delayed MBNNs with discontinuous activation functions. Based on the framework of Filippov solution and differential inclusion theory, using new analytical techniques and introducing suitable Lyponov functionals, some novel sufficient conditions ensuring the exponential synchronization of considered networks are established via two types of discontinuous controls: linear feedback control and adaptive control. In particular, we extend the discontinuous control strategies for neural networks with continuous dynamics to MBNNs with discontinuous activations. Numerical simulations are given to show the effectiveness of the theoretical results. Our approach and theoretical results have a leading significance in the design of synchronized MBNN circuits involving discontinuous activations and time-varying delays.The final chapter investigates the general decay synchronization(synchronization with general decay rate) MBCGNNs with discontinuous activation functions and mixed time-varying delays. Based on the framework of Filippov solution and differential inclusion theory, using novel analytical techniques and constructing suitable Lyapunov functionals, some novel sufficient conditions ensuring the general decay synchronization of considered CGNN are established via two types of nonlinear controls. The general decay synchronization contains polynomial synchronization, exponential synchronization, and other synchronization as its special cases. Finally, two numerical examples are given to show the feasibility of the theoretical results. The results of this paper extend the discontinuous control strategies for neural networks with continuous dynamics to MCGNNs with discontinuous activations.