【作者】 谭晓惠；

【导师】 杨翊仁；

【作者基本信息】 西南交通大学 ， 一般力学与力学基础， 2002， 硕士

【摘要】 神经网络的研究至今已有近40年的历史，本文在第一章绪论中综述了神经网络的发展历史，并重点论述了动态神经网络的发展现状及趋势。 由于动态神经网络系统在联想记忆、最优化、图象处理等方面广泛的应用前景，使得微电子学家、物理学家、数学家、神经科学家、生物学与心理学家、控制理论家、计算机科学家和人工智能专家等都热情地投入这一领域。但是以往所提出的该类神经网络模型都假设自反馈项为线性的，不能真实的反映其本质，所以在本文的第二章将对原有的动态神经网络模型进行推广，并研究推广模型的一些基本特性。第二章分两种方法对其进行研究。第一种是通过引入非线性测度的概念，分别对激励函数采用了两种不同的Lipschitz连续假设，给出这两种不同连续假设下神经网络系统的全局指数稳定性条件，并分析其指数收敛率。第二种是采用李雅普诺夫直接方法，在激励函数的Lipschitz连续假设下，得到了两个全局指数稳定的充分性判据。 到目前为止，被人们广泛采用的神经网络模型主要分为以下两类：连续型神经网络和离散型神经网络。然而，现实生活中的确存在一些神经网络，它们既不属于第一类也不属于第二类。它们的共同特点是在某些特定的瞬间会发生突变。而这些系统的突然的尖锐的变化多是以脉冲的形式出现的。因此，本论文在第三章基于动态神经网络引入了一类新的神经网络系统——时变时滞脉冲神经网络系统，通过分析，得到了其全局指数稳定的充分性判据。 最后，在第四章，将利用前面所得到的关于神经网络全局指数稳定的一些判据来求解最优化问题。通过具体的算例，发现将神经网络全局指数稳定的一些判据用来求解最优化问题均能达到预期的结果。更多还原

【Abstract】 It has been 40 years since neural networks were first introduced. In chapter one of this paper,neural networks’ development history is summarized and emphasis is current development situation of dynamic neural networks.Because of dynamic neural networks’ brilliant application prospect on associative memory,optimization,image processing and so on,many physicians,mathematicians et. are devoted to the study on this field. But all the models of neural networks before are assumed that self-feedback is linear which can not reflect the essentiality of the neural networks. So in chapter two of this paper,the self-feedback is improved and can be nonlinear. Moreover,basic features of this kind of neural networks are investigated. Two different methods are used in chapter two to analyze the features. First by introducing nonlinear measures,the existence,uniqueness and global exponential stability of the equilibrium point of this kind of neural networks are investigated. Two different Lipschitz continuous activations are considered. Some sufficient conditions and convergence estimate for global exponential stability of neural networks are obtained on condition that self-feedback is nonlinear. Second by using Liapunov direct method,two different sufficient global exponential stability conditions are obtained on condition that activation functions are Lipschitz continuous.So far,the most widely used neural networks are classified into two groups:continuous and discrete networks. However,in the real world there are many networks which belong to neither of the groups mentioned above. They are characterized by abrupt changes of states at certain instants. Many sudden and sharp changes occur in the form of impulses. Therefore it is important to investigate impulsive networks. Based on the structure of the dynamic neural networks,in chapter three of this paper the delayed impulsive neural network model is introduced. Based on analysis,sufficient conditions which ensure the exponential stability of this new neural networks are obtained.At last,in chapter four,several sufficient conditions which ensure theexponential stability of neural networks are used to solve optimization problems. By computing specific examples,it is found that those sufficient conditions are effective in solving optimization problems.更多还原