【作者】 常茹；

【导师】 夏茂辉；

【作者基本信息】 燕山大学 ， 运筹学与控制论， 2010， 硕士

【摘要】 近年来,Hopfield型神经网络得到了广泛地研究,并且成功地应用于信号处理、模式识别、组合优化等领域。由于具有时滞的Hopfield型神经网络在解决动态图像处理等问题上有较重要的应用,因此,具有时滞的Hopfield型神经网络的研究更受到许多学者的关注.神经网络的稳定性是一个关键问题,有些应用要求神经网络模型是全局渐近稳定的,即对应的动力系统的每一个解收敛到平衡点。论文在已有文献的基础上,通过对稳定性理论和神经网络的研究,基于Lyapunov泛函的思想,选取一个适合神经网络模型的Lyapunov函数,并通过一些处理矩阵不等式的技巧,对选取的Lyapunov函数求导放缩,最终得到一个保守性更好的线性矩阵不等式的结果,包括时滞神经网络全局渐近稳定和全局指数稳定。近些年神经网络稳定性方面的研究成为热点,已有的文献对时滞细胞神经网络稳定性的研究大都限于时滞无关的结果,如何建立时滞相关的稳定性判据就成了热点问题。本文对时滞相关进行了研究,得出了一些有益的结论,同时论文中的时滞相关的结果还可以推出时滞无关的结果。最后对二阶Hopfield型神经网络稳定性进行了分析,这是对高阶神经网络稳定性研究的初步探讨。在数值算例中,通过Matlab中的LMI工具箱和Simulink图像仿真器做出数值仿真与图像仿真,验证了结果的正确性。更多还原

【Abstract】 In recent years, the Hopfield neural network has been widely studied, and has already been successfully applied to signal processing,pattern recognition,combination optimization and so on. Because the Hopfield neural network with time delays has important application in solving the problem of dynamic image processing Therefore, A study on Hopfield neural network with time delays has been paid close attention by many scholars.Stability is a key issue in applications of neural networks.In some applications, it is desirable that the network possesses a unique and globally asymptotically stable equilibrium point for every external input. In researching this thesis, we choose a Lyapunov function to suit neural networks, through in theory of stability and neural networks, and then dispose the matrix with some skills. We get a better liner matrix inequality result, including global asymptotically stability and global exponential stability of time delays neural network. In these years, stability analysis of neural network turns to be hotspot, but most of existing results derived in the literature are independent of the delay parameters, how to propose a delay-dependent stability criterion for delayed cellular neural networks is a hot problem. In this thesis we present delay-dependent stability criterion, so as to get the maximum numerical delay and some results independent of the delay parameters easily. And more, stability analysis of a second order neural network of Hopfield in this paper is a new task, which is an experiment in stability analysis of high order neural network. At last, we present numerical examples to illustrate the validity of the results.更多还原