The Analysis Of Stability And Passivity For Recurrent Neural Networks

The recurrent neural networks has considerable improvement since the Hopfield neural networks, energe function and the stability of networks was proposed in1982. The dynamic behavior of recurrent neural networks has been extensive applications in associative memory, optimization, pattern recognition and so on. The stability of dynamics system is the basis of complicated dynamic behavior. So, the stability analysis of recurrent neural networks has important significance.The passivity is an significant tool to analyze and design nonlinear system. From the point of energy, the system can be analyzed and designed by using the characteristic of the input and output, the energy is described by input and output. The passivity theory provide a new method for the construction of Lyapunov functional. The Lyapunov functional is generally applied to control problem. However, there are few of feasible way to construct the Lyapunov functional. In fact, the storage function of passivity system can become the Lyapunov functional under certain conditions. So, the passivity theory can be used to study the stability of system just like Lyapunov functional does. The passivity theory is an effective tool to investigate the stability of system.In this dissertation, we deal with the problem of stability and passivity for recurrent neural networks. The main contents are summarized as follows:(1) Firstly, the history and basic characteristic of neural networks is discussed; Then, the recurrent neural networks is summarized, at the same time, several usual models of recurrent neural networks and their applications are listed. Secondly, we illustrate the background and significance for the stability of recurrent neural networks. Then, the background and significance of passivity theory is presented. Furthermore, some notations and lemmas are given in this chaper. Finally, the main work of this dissertation is pointed out.(2) The problem of delay-dependent robust stability for Hopfield neural networks of neutral-type is investigated. The neural networks considered is different from the others, which has different time-varying delays in discrete and neutral terms. The descriptor model transformation approach combines with a new class of Lyapunov-Krasovskii functional to ensure a large upper bound for time delay. The delay-dependent robust stability criterion is formulated in terms of linear matrix inequalities, in which the restriction of the derivative of time-varying delay in discrete terms is removed. Since both the discrete-delays and neutral-delays are taken into account, the obtained stability criterion is more general than some existing ones which are dependent on the same delays in discrete and neutral terms. Numerical examples are given to illustrate the effectiveness of the proposed methods.(3) The problem of delay-dependent robust stability for bidirectional associative memory neural networks of neutral-type is investigated. The neural networks considered with time-varying delays and parameter uncertainties. A less conservative stability criterion is obtained by using suitable Lyapunov-Krasovskii functional and the descriptor model transformation approach. The free-weighting matrix approach is applied to avoid the restriction of the derivative of the time-varying delay is less than1. Delay-dependent robust stability criterion is proposed in terms of linear matrix inequalities, which can be solved by MATLAB LMI Control Toolbox. Numerical examples are given to illustrate the obtained criterion is less conservativeness than some existing ones.(4) The problem of passivity for recurrent neural networks with time-varying delay and parameter uncertainties is investigated. The recurrent neural networks considered is composed of different activation function and it is the generalization of Hopfield neural networks. The equivalent descriptor model transformation is used to ensure a less conservative passivity criterion. The passivity criterion is obtained while a given definition of passivity prevails and the conclusion is applied to Hopfield neural networks. The passivity criterion is formulated in terms of linear matrix inequalities and the restriction of derivative of time-varying delay is less than1is removed. Two numerical examples are given to illustrate the effectiveness of our methods.(5) The problem of robust passivity for discrete-time standard neural network model with time-varying delays and norm-bounded parameters uncertainties is investigated. The model is the interconnection of a linear dynamic system and static nonlinear operators consisting of bounded activation functions. The discrete-time standard neural network model is applied to analyze the passivity of discrete-time recurrent neural networks and synthesize the state-feedback passive controller for discrete-time nonlinear system modeled by the neural networks. By constructing suitable Lyapunov-Krasovskii functional, the delay-dependent passivity criterion for discrete-time delayed standard neural networks model is obtained in terms of linear matrix inequality. Numerical examples are given to illustrate the effectiveness of the proposed methods.(6) The problem of robust passive control for nonlinear system based on delayed standard neural network model (DSNNM) is investigated. Firstly, we deal with the passivity of the DSNNM without external input. The delay-dependent passivity criterion with dissipation η is given by using suitable Lyapunov-Krasovskii functional and free-weighting approach. Then, based on the delay-dependent passivity criterion, the state-feedback passive controller which ensure the close-loop system is robustly passive are designed for DSNNM. The maximum dissipation η can be solved by using the solver of gevp in LMI Control Toolbox of MATLAB. Numerical example and simulation result is given to illustrate the effectiveness of the proposed methods.(7) The research work of this dissertation is summarized, and the prospect of my future research are given.