随机神经网络的几乎必然指数稳定性分析

发布时间：2018-06-01 14:14

本文选题：随机神经网络 + 脉冲随机神经网络　；参考：《安徽大学》2017年硕士论文

【摘要】：由于神经网络在众多学科中都有着极其广泛的应用,从而吸引了越来越多的学者对其进行研究.然而,在实际系统中难免会受到随机扰动和脉冲的影响,这样可能会破坏系统的稳定性.因此,着眼于研究神经网络的平衡点的稳定性非常重要.本学位论文系统地研究了随机神经网络、脉冲随机神经网络的稳定性问题.通过构造Lyapunov函数,利用It(?)微分公式,运用随机分析技巧结合线性矩阵不等式(LMI),得到了随机神经网络和脉冲随机神经网络几乎必然指数稳定的重要定理.本论文主要包括以下几部分:1.绪论部分介绍随机神经网络的研究背景及研究意义,并概述了随机神经网络稳定性的研究进展,给出预备知识.2.研究了一类随机神经网络几乎必然指数稳定性的问题.首先,我们利用Lyapunov稳定性理论、运用随机分析技巧、It(?)微分公式得到LMI形式的m-维随机神经网络几乎必然指数稳定的定理.其次,稳定性分析的基础上,结合一些不等式技巧,得到系统中含有不确定项的m-维随机神经网络几乎必然指数稳定的充分条件.最后,给出的数值仿真实例证明本章结论的有效性.3.考虑了更实际的数学模型:一类带有脉冲的随机神经网络.首先,给出脉冲随机神经网络几乎必然指数稳定的定义.接下来,运用Lyapunov函数法、指数鞅不等式、BoreI-Cantelli引理等得到脉冲随机神经网络几乎必然指数稳定的一系列条件.最后,给出的数值仿真实例说明本章结论的有效性.最后,对全文进行总结并提出接下来有待研究的问题.
[Abstract]:Neural network is widely used in many disciplines, which attracts more and more scholars to study it. However, it is inevitable to be affected by random perturbations and impulses in practical systems, which may destroy the stability of the systems. Therefore, it is very important to study the stability of the equilibrium point of neural network. In this dissertation, the stability of stochastic neural networks and impulsive stochastic neural networks is studied systematically. By constructing Lyapunov function, we use it By using stochastic analysis technique and linear matrix inequality (LMI), the important theorems of exponential stability of stochastic neural networks and impulsive stochastic neural networks are obtained. This paper mainly includes the following parts: 1. The introduction part introduces the research background and significance of stochastic neural network, summarizes the research progress of stochastic neural network stability, and gives the preparatory knowledge. The problem of almost certain exponential stability of a class of stochastic neural networks is studied. First of all, we use the Lyapunov stability theory and the random analysis technique. The theorem of exponential stability of m- dimensional stochastic neural networks in LMI form is obtained by differential formula. Secondly, on the basis of stability analysis and some inequality techniques, sufficient conditions for almost exponential stability of m- dimensional stochastic neural networks with uncertainties are obtained. Finally, a numerical simulation example is given to prove the validity of the conclusion. 3. A more practical mathematical model is considered: a class of stochastic neural networks with impulses. Firstly, the definition of exponential stability of impulsive stochastic neural networks is given. Then, using the Lyapunov function method, the exponential martingale inequality and the BoreI-Cantelli Lemma, a series of conditions for the exponential stability of impulsive stochastic neural networks are obtained. Finally, a numerical simulation example is given to illustrate the validity of the conclusion. Finally, the full text is summarized and the problems to be studied are put forward.
【学位授予单位】：安徽大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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