| In recent years,research into static neural networks has received significant attention due to their successful application in system modeling,adaptive control,pattern recognition and prediction.In the practical application of neural networks,the time delay caused by the limited switching speed of amplifiers and the inherent transmission time of neurons is inevitable.Its existence will cause the oscillation,chaos and even instability of the system.On the other hand,due to the high degree of interconnection of massive neurons and the inevitable effects of external noise interference during the acquisition and measurement of data by sensors,only part of the neuron state information can usually be output through the network.As one of the important state estimation methods,H_∞state estimation introduces the index of H_∞norm in the design of state estimator.This method does not require the statistical characteristics of noise signal to be known,and realizes the goal of estimating system state based on measured signal.Therefore,in recent years,the H_∞state estimation of static neural networks under the influence of time delay has gradually become a hot research field.Based on the existing research,the main research contents of this paper are as follows:(1)The H_∞state estimation problem of a class of static neural networks with time-varying delay is investigated.Firstly,in order to fully utilize the delay boundary and derivative information,an innovative Lyapunov-Krasovskii(L-K)functional is developed,which includes delay-product-type(DPT)terms both in the non-integral and single integral functionals,and the S-dependent integral term is introduced to combine with the single integral DPT functional for the first time.Then,the generalized free-weighting-matrix integral inequality and other methods are selected to coordinate effectively with the constructed L-K functional,and the estimator design conditions with less conservative are obtained.Finally,a more general gain inverse solution is given,and the gain matrix independent of the activation function is obtained,which removes the qualification that the activation function must be reversible.(2)The H_∞state estimation problem for a class of mixed time-varying delay networks is studied.Firstly,a new static neural network system model with state time-varying delay and output time-varying delay is established considering the factors such as long signal transmission time and limited channel transmission capacity.Based on this model,an improved proportional integral(PI)estimator with exponential gain is proposed.In addition,the L-K functional constructed contains not only two kinds of time-varying delays,but also single integral type asymmetric functional,which relaxes the requirement for the quadratic term to satisfy the positive definite condition.In order to make full use of delay boundary information and derivative information,an improved Integral Inequality Based on a Nonorthogonal Polynomial Sequel improved by delay dependent matrix is proposed,and a delay dependent matrix is introduced,which reduces the conservatism effectively.Thus,the asymptotic stability of the estimation error system under the given anti-interference index is guaranteed.(3)The problem of H_∞state estimation for a class of static time-varying delay neural networks with incomplete information is studied.Firstly,a more general improved Arcak-type state estimator is constructed,which takes into account the random fluctuation of estimator gain.In addition,in order to make full use of the slope information of the activation function,the estimation error of the activation function is cleverly divided into two parts.The new L-K functional can effectively capture the slope information of the activation function,and the functional also includes the DPT functional with negative definite term.Then,the improved interactive convex combinatorial integral inequality is used to effectively match the constructed functional.Finally,the stability criterion with low conservatism and the design conditions of estimator are obtained.Finally,the work of this paper is summed up,and the promising future of the state estimation problem for delayed neural networks is expected.There are 4 figures,16tables and 117 references. |
