Researches On Stability And Synchronization For Several Categories Of Higher-Order And Memristor-Based Neural Networks

Artificial neural networks have been one of the research hotspots in the field of artificial intelligence since 1980 s.It abstracts the human brain neuron network from the perspective of information processing,establishes a simple mathematical model,and forms different networks according to different connection modes.With the continuous in-depth study of many scholars,neural networks have made great progress.They have shown good performance in many fields,such as automatic control,intelligent robots,prediction and estimation,intelligent computing,image processing and pattern recognition,and so on.On the one hand,higher-order neural networks have great advantages over lower-order neural networks in approximation performance,storage capacity,convergence speed and fault-tolerant ability.These merits can be applied to parallel computing,adaptive pattern recognition and optimization problems.On the other hand,because of the high storage capacity,small size and non-volatility of memristor,memristor-based neural networks have attracted extensive attention in the fields of signal processing,reconfigurable computing,programmable logic and control system based on brain-computer interfaces.In the last few years,the dynamic behavior of neural networks has been deeply studied,especially the stability and synchronization problems.The main objectives of this dissertation are to investigate the existence and stability of equilibrium point,periodic solution and almost automorphic solution of two kinds of high-order bidirectional associative memory(BAM)neural networks as well as the stability of equilibrium point,periodic solution of two types of memristor-based neural networks and synchronization phenomena of their drive-response systems,respectively.Furthermore,by using the universal approximation theory of neural networks or fuzzy logic systems,we will study the adaptive fuzzy tracking control problems for two kinds of uncertain fractional-order nonlinear systems.The main contributions of this dissertation can be summarized as follows:1)The global exponential stability of equilibrium point and periodic solution for impulsive fuzzy high-order BAM neural networks with continuously distributed delays is investigated.By applying the inequality analysis technique,M-matrix and Banach contraction mapping principle and constructing some suitable Lyapunov-Kravsovskii functionals,some sufficient conditions for the existence,uniqueness and global exponential stability of equilibrium point and periodic solutions are established.In addition,three examples with numerical simulations are presented to demonstrate the feasibility and effectiveness of the theoretical results.2)The existence and global exponential stability of almost automorphic solution for neutral type high-order Hopfield BAM neural networks with time-varying leakage delays on time scales are considered.The main methods relay on the exponential dichotomy theory on time scales,Banach contraction mapping principle and differential inequality analysis techniques.In the addressed system,we not only consider the effects of the first-order neutral terms on neural networks,but also investigate the influences of the second-order neutral terms on the neural networks.High-order Hopfield BAM neural networks with continuously distributed leakage delays on time scales are also considered.Our results are completely new even if time scale T = R or T = Z and complementary to the previously existing results.Finally,three examples with numerical simulations are presented to illustrate the feasibility of our proposed theoretical results.3)The stability and synchronization problem for a class of memristor-based neural networks with both time-varying and continuously distributed delays is considered.By using the homeomorphism theory,delay differential-integral inequality technique and appropriate Lyapunov-Kravsovskii functional,some sufficient conditions for global exponential stability of equilibrium points of some new memristor neural networks and synchronization of drive-response systems are obtained.under the framework of Filippov solution.On the other hand,we investigate the stability of periodic solution for a class of memristor-based Cohen-Grossberg-type BAM neural networks with time-varying delays and continuously distributed delays.By using the Banach contraction mapping principle and impulsive delay differential-integral inequality,some sufficient conditions ensuring the existence and global exponential stability of periodic solution are derived.The proposed method can also be applied to study the impulsive memristor-based Cohen-Grossberg-type BAM neural networks with timevarying delays and finite distributed delays.In two kinds of problems,the exponential convergence rate can be estimated by solving inequalities.Finally,some examples with numerical simulations are given to demonstrate the practicability of our given results and an application of the obtained theory is presented in the pseudorandom number generator.4)The stability and lag synchronization for memristor-based fuzzy Cohen-Grossberg-type BAM neural networks with mixed delays(asynchronous time delays and continuously distributed delays)and impulses are investigated.By applying the inequality analysis technique,homeomorphism theory and some suitable Lyapunov-Kravsovskii functionals,some new sufficient conditions for the uniqueness and global exponential stability of equilibrium point are established.Furthermore,we obtain several sufficient criteria concerning globally exponential lag synchronization for the proposed system based on the framework of Filippov solution,differential inclusion theory and control theory.In addition,some examples with numerical simulations are given to illustrate the feasibility and availability of obtained results.5)A class of uncertain single-input-single-output non-strict feedback fractional-order nonlinear systems are considered.Fuzzy logic systems(FLSs)are employed to approximate the unknown nonlinear functions and model the uncertain fractional-order nonlinear systems.For the states measurable case,an adaptive fuzzy state feedback control scheme is developed under the framework of the backstepping technique.For states unmeasurable case,an observer-based output-feedback control design is proposed by introducing a serial-parallel estimation model and using the dynamic surface control technique.Under the drive of the reference signals,the semi-globally uniform ultimate boundedness for all the signals and the tracking errors to a small neighborhood of the origin are proved based on using Lyapunov function theory and choosing appropriate design parameters.Two examples with numerical simulations are presented to illustrate the availability of the proposed control approaches.6)The adaptive fuzzy fault-tolerant tracking control problems for a class of uncertain nonaffine nonlinear fractional-order multi-input single-output systems with actuator failures and full-state constraints are investigated.Based on the implicit function theorem and mean value theorem,the design difficulty arising from nonaffine nonlinear terms is surmounted.Then,the unknown ideal control inputs can be approximated by using some suitable FLSs.An adaptive fuzzy fault-tolerant control(FTC)algorithm is developed by constructing the barrier Lyapunov functions and estimating the compounded disturbances.Moreover,it is proved that under the drive of the reference signals,all the signals in the closed-loop system are semi-global uniformly ultimately bounded and all the states of nonaffine nonlinear fractional-order systems are guaranteed to remain in the predetermined compact set.Finally,two examples with numerical simulations are presented to illustrate the availability of the proposed adaptive fuzzy FTC approach.This dissertation mainly studies theoretically the stability and synchronization of several kinds of high-order and memristor neural networks as well as the adaptive control of two kinds of uncertain fractional-order nonlinear systems.All the results obtained in this dissertation have been tested by numerical simulation.Finally,the main research conclusions of this dissertation are summarized and the future research directions are prospected.