Research On Synchronization Of Fractional Order Neural Networks Under Non-ideal States

In recent decades,the research of fractional calculus has no longer focused on pure math-ematical theory,but begins to expand to many fields of science and engineering.As one of the important branches,the synchronization of fractional order neural networks has gradually become a research hotspot.Due to the actual environmental conditions of network communi-cation,when establishing the model of engineering problems,we have to consider the existence of many factors that have an adverse impact on network communication.Therefore,it is worth considering to design an appropriate control mechanism to ensure that the network can achieve synchronization when it is in a non ideal state.This paper mainly models the fractional order neural networks affected by the parameter uncertainty caused by the aging of instrument parts,the inevitable time delay and the random network attack behavior,designs appropriate con-trollers respectively,analyzes the synchronization according to the Lyapunov stability theory,and gets the sufficient conditions for the system to achieve synchronization,Then the feasible solution is obtained with the help of Matlab’s LMI toolbox or Yalmib toolbox.Finally,the net-work model is numerically simulated with fractional predictor correction algorithm.The main contents of the full text are as follows:The first chapter briefly describes the research background of fractional order neural net-work,the research background of network synchronization and the research status of fractional order neural network synchronization.Some fractional calculus phenomena in real life are in-troduced into the study of fractional neural network.The second chapter focuses on the introduction of the basic definitions and theorems used in this paper,as well as the brief description of the fractional predictor correction algorithm and the symbols used,which lays a foundation for the synchronization researches of fractional neural networks in Chapter 3 and Chapter 4.In Chapter 3,the asymptotic synchronization of uncertain fractional order neural networks with leakage delay and random time-varying delay is studied.It not only considers no delay and random time-varying delay in the activation function,but also considers no delay and leakage delay in the neuron itself.At the same time,it also takes into account the parameter uncertainty caused by the aging of instrument parts.According to Lyapunov stability theory,the sufficient conditions for the stability of error system are obtained.Finally,two numerical simulation ex-amples are given to verify the effectiveness and feasibility of the method.In Chapter 4,we study the adaptive event-triggered synchronization problem of uncertain fractional order neural networks with double deception attacks and time-varying delay.In this chapter,the adaptive event triggering mechanism is used to transmit the necessary information to model the fractional order neural network that may be attacked by deception attacks from sen-sor to controller and from controller to actuator,and the occurrence model of deception attacks are designed as Markov variables.According to the Lyapunov stability theory,the sufficient conditions for the stability of the error system are obtained.Finally,the effectiveness and fea-sibility of the method are verified by two numerical simulation examples.The fifth chapter summarizes the main contents and achievements of this paper,and briefly describes the problems to be further solved in the research of fractional order neural network and the personal research direction in the future.