Research On State Estimation For Continuous Neural Network

In recent years,with the rapid development of neural network and it has been more and more applicationed in the field of engineering,but in the actual engineering application,some phenomenon will appeared inevitably,such as non-fragility,nonlinear,time delays and other issues,these problems will directly lead to only part of neurons state information could through the network output.Thus,it has been important scientific value and practical significance to estimate accurately the state of neurons as far as possible.The content of this paper is to model the continuous neural network system,and based on the Lyapunov stability theory,combined with linear matrix inequality(Linear Matrix,Inequality,LMI)technology,the technique of matrix analysis,the stability of the system will be discussed and the design method of the non-fragile state estimator will be verified.First of all,according to the neural network system with time-varying delays,the system's stability will be analysised,and the research method of non-fragile state estimator considering additive gain variations will be discussesed.Using the LMI method,the sufficient conditions of the non-fragile state estimator will be obtained,which guaranteed the system asymptotic stability and satisfied other constraints,and the gains of the non-fragile state estimator,and the results would be analyzed.Secondly,a continuous neural network model with additive gain variations and time-varying delays is established,system's stability is analysised and the non-fragile state estimator is designed.After defining the augmented system of the continuous neural networks and the constraints,the Lyapunov functions which accordance its stability theory are selected,the sufficient conditions are obtained by analyzing which guarantees the augmented system achieves the asymptotic stability and state estimator gains.At this time,the non-fragile state estimator design method has been transformed into the feasible solution to solve the corresponding LMIs.Thirdly,the stability and non-fragile state estimation algorithm for neural networks with time-varying delays are studied.The multiplicative norm bounded estimator gain variations are adopted,the neuron-state-dependent nonlinear perturbation is described by the Lipschitz condition,and the non-fragile state estimator is investigated.The sufficient conditions for the existence of the desired non-fragile state estimator is obtained by using Lyapunov stability theory,matrix analysis technology,LMI technology and Leibniz-Newton formula,and the feasible solution of the standard LMI problem.Finally,the stability and non-fragile state estimation algorithm for continuous-time neural network system with noises are studied.Two different functions are used to express noises,namely the noise sequence produced by the system and observation noise sequence of the system.Combining with the aforementioned neural network model,the non-fragile state estimator with gain variations are designed.By analyzing the stability and H? performance of the error dynamic augmented system,the linear matrix inequalities are acquired which need to be satisfied for the existence of desired the non-fragile state estimator,namely,the non-fragile state estimator design is transformed into a convex optimization problem which can be solved by the standard LMI method,and the accuracy of the research is illustrated by the actual example.