Stability And Synchronization Of Several Types Of Memristor-based Fractional-order Neural Networks

Along with the development of neural network technology,neural networks have been widely used in information communication and other engineering fields.The growing importance of neural networks makes them become an important topic around the world.Compared with traditional calculus,the infinite memory of fractional-order calculus makes it more accurate in describing viscous systems and other practical models.Furthermore,the combination of fractional-order calculus and memristive neural networks is more consistent with real problems,the value and practical meanings are in focus.This dissertation focuses on several types of fractional-order memristor-based neural networks.By utilizing fractional-order calculus theory,Lyapunov stability theory and other methods,the stability and synchronization of multiple delayed fractional-order memristive neural networks,fractional-order fuzzy cellular memristive neural networks have been investigated,as well as the robust stabilization of fractional-order memristive neural networks with disturbances.The specific researches are as follows:1.The uniform stability and asymptotic stability problems of multiple delayed fractional-order memristive neural networks are studied.Multiple delays may occur between different neurons,the single delay cannot meet the practical needs.Firstly,the existence and uniqueness of equilibrium point are derived by using comparison mapping,and it's unnecessary to consider the boundary of the activation function.Secondly,based on the Lyapunov indirect method,the inequality technique and free weight parameter approach,some less conservative stability results are presented.The numerical examples show the effectiveness of the obtained results.2.The exponential stability problem of multiple delayed fractional-order fuzzy cellular memristive neural networks is discussed.Firstly,by employing the Laplace transform method,theory of complex-variable functions and theory of stability,a novel exponential stability is derived.Secondly,the fractional-order comparison lemma and the new exponential stability criteria are used to obtain sufficient conditions for exponential stability of the studied fractional-order neural networks.The main advantage of the proposed method is that more general stability results can be derived by only constructing the Lyapunov functional in quadratic form.Besides,those results can deal with all the situations of constant delay systems.Compared with the existing stability conditions of the same type of neural networks,this thesis generalizes the results to exponential stability,and the obtained results are more general.Finally,The effectiveness and superiority of the proposed method are verified by simulations.3.The synchronization problems of fractional-order fuzzy cellular memristive neural networks with constant delays and time-varying delays are considered,respectively.The original system is transformed into a right-hand continuous system by using approaches of Filippov differential inclusion,measurable selections,and interval matrix.Then,the feedback controller and the fractional-order adaptive controller are designed to obtain conditions on exponential synchronization,Mittag-Leffler synchronization and asymptotic synchronization of fractional-order memristive neural networks.Finally,the practicability and the effectiveness of the synchronization results are verified by simulations.4.The robust stabilization problem of fractional-order memristive neural networks with disturbances is solved.Without loss of generality,the idea of equivalent-inputdisturbance is firstly introduced through a delayed fractional-order nonlinear system with uncertainties and disturbances.Secondly,by employing the equivalent-input-disturbance method to regard the disturbances,delays,nonlinear terms and uncertain terms in the system as a total disturbance,and along with stability theory,robust stabilization criteria of fractional-order memristive neural networks with disturbances are derived in terms of linear matrix inequalities.Lastly,the numerical examples show the effectiveness of the robust stabilization results.