Synchronization Control And State Estimation For Complex-valued Neural Networks With Time Delay

Artificial neural network is a complex network system that explores the structure,function and dynamic behavior of the brain nervous system by modeling brain neurons.Complex-valued neural networks,as the networks that deal with information in the complex domain with complex-valued variables,have received widespread attention.Not only is it a simple theoretical generalization of the real-valued case but also the involvement of the complex-valued activation functions and complex-valued weights allows the functionality of a single basic neural processing element and of a network to be expanded,so that complex-valued neural networks have better performance than real-valued neural networks.There exist some complex application scenarios where complex-valued neural networks are either inevitably required or more effective than real-valued neural networks.Typical applications include XOR and the detection of symmetry problem.Its application has been involved in many aspects of production and life,such as image processing,associative memory and traffic power system.Different application requirements correspond to special dynamical behaviors.Due to the time required for the information transmission of the interaction between neurons and the limitations of physical components,such as the switching speed of amplifiers,the phenomenon of time delay widely exists in network systems,which may affect the system performance and stability.Therefore,based on the characteristics of complex-valued neural networks,it is of great theoretical significance and practical value to explore the analysis and control of complex-valued neural networks with delay and apply them to practical problems.In this thesis,based on two different types of activation function,the problems of state estimation and synchronization control of delayed complex-valued neural networks are further studied by utilizing sliding mode control theory,stochastic control theory,finite/fixed-time control theory and linear matrix inequalities approach.The main contents are as follows:1.The synchronization control problems of delayed stochastic complex-valued neural networks are studied.Firstly,considering the activation function in which the real and imaginary parts are explicitly expressed,the system is transformed into equivalent realvalued system by separating the real and imaginary parts of the system.By means of Lyapunov stability theory,Halanay inequality and stochastic analysis technique,a criterion of p moment exponential anti-synchronization for stochastic complex-valued neural networks with constant time delay are given.Secondly,the influence of timevarying time delays and mismatched parameters is taken into account.The whole analysis process is carried out under the framework of complex domain without separating the real and imaginary parts.Based on complex version It? formula,a valid state feedback controller is designed to achieve the quasi-projective synchronization between drive and response system.The synchronization error bound is also estimated.The usefulness of the prosed method is illustrated by simulation examples.2.For complex-valued inertial neural networks with time-varying discrete delay,distributed delay and external disturbance,sliding mode synchronization control problems are studied by using the direct method without separating the real and imaginary parts of the system.Firstly,considering the unknown external disturbance,the system is transformed into a first-order system by variable transformation.A nonlinear disturbance observer is designed to estimate disturbance,and a suitable sliding mode surface is designed.By constructing an appropriate Lyapunov-Krasovskii functional and using linear matrix inequality technique,sufficient conditions are given to ensure the synchronization of the driving-response systems without requiring differentiable delays.An effective sliding mode controller based on the observer is designed to ensure that the state of the error system can reach the sliding mode surface in a finite time.Secondly,taking into account parameter uncertainties,the idea of direct analysis is developed without exploiting order reduction.An appropriate sliding mode surface and sliding mode controller are designed to make the driving-response system achieve synchronization and the sliding mode dynamic has strict(Q,S,R)-λ-dissipative performance.Several simulation verifications are provided,including numerical simulations based on two type of activation functions,as well as applications of the approach to a Pseudorandom Number Generator and image encryption exercise.3.The problem of fixed time synchronization for a class of delayed complex-valued neural networks with inertial term are studied.Assuming that the activation function satisfies different assumptions,the system is transformed into a first-order system by variable transformation.Two different controllers are designed,under which the addressed network systems can achieve synchronization perfectly in a fixed time.The corresponding synchronization criteria and the estimates of the settling times are derived by using separation and direct methods,respectively.Different from the existing results,the power of the designed controller is independent.Finally,based on two types of activation functions,simulation examples are given to verify the effectiveness of the proposed method.4.The finite time state estimation problem of complex-valued bidirectional associative memory neutral-type neural networks with time-varying delays is studied.By resorting to the Lyapunov function approach,the Wirtinger inequality and the reciprocally convex approach,a delay-dependent criterion in terms of LMIs is established to guarantee the finite-time boundedness of the error-state system.An effective state estimator is designed to estimate the network states through the available output measurements.Finally,a numerical example is presented to demonstrate the effectiveness of the proposed results.