Research On Synchronization Of Fractional-order Memristor-based Neural Networks

In recent years,neural network has become an important research topic owing to its wide application in pattern recognition,optimization,signal transmission and other fields.As the fourth generation circuit element that describes the relationship between current and magnetic flux,memristor can act as the synaptic weight between neurons.By introducing it into neural networks,memristor-based neural networks(MNNs)can be constructed to simulate human brain.Compared with integer-order calculus,the fractional-order one shows infinite memory and heredity,and can describe physical and engineering problems more accurately.With the deepening of research field and content,researchers found that the neural networks in real number domain have limitations in processing some multidimensional data.Based on the real and complex fields,the quaternion-valued networks have attracted the attention of many scholars and become a heated research topic in recent years due to its efficient processing ability of multidimensional data.On the basis of the above analysis,this paper combines the fractional-order theory with MNNs,and discusses several kinds of the synchronization control problems in real and quaternion domains respectively.Firstly,the finite-time synchronization of the corresponding real domain is analyzed in terms of the state feedback control strategy,then this method is applied to the quaternion domain based on the results of the real domain.Meanwhile,a kind of adaptive controller is designed,using the properties of fractional-order inequality and Mittag-Leffler function,the adaptive synchronization and Mittag-Leffler synchronization of the studied system are realized.The main research contents of the thesis are as follows:(1)Based on the theory of set-valued mapping and differential inclusion,the finite-time synchronization of fractional-order real-valued MNNs system is studied,in which the discontinuous activations and multiple delays are concerned.By designing the state feedback controller,making use of fractional stability theorem,comparison principle and fractional differential inequality,the sufficient conditions with respect to finite-time synchronization are analyzed and derived.In addition,the upper bound of the synchronization can be obtained and optimized by adjusting the control parameters appropriately.(2)Considering that the quaternion-valued neural networks possess the ability to process multi-dimensional data efficiently,the finite-time synchronization capability based on quaternion domain and fractional-order neural networks system is analyzed,in which the state feedback control strategy is considered.In terms of Hamilton rule,the studied system model is divided into four real-valued networks and the new synchronization conditions of the corresponding quaternion domain are derived.(3)Aiming at a class of fractional-order quaternion-valued MNNs synchronization problem,considering the control gain and time delay,two general adaptive control schemes are designed,in which the synchronization speed can be flexibly adjusted with the change of control gain.Firstly,sufficient conditions are developed to ensure the asymptotic synchronization by applying Lyapunov functions,some fractional derivative inequalities and comparison theorem.On the basis of the above results,the Mittag-Leffler synchronization of drive-response systems is further proved in terms of Razumikhin technique and Mittag-Leffler function property.