【作者】 王鹏；

【导师】 黄创霞；

【作者基本信息】 长沙理工大学 ， 应用数学， 2014， 硕士

【摘要】 近年来,由于神经网络在模式识别、智能计算、联想记忆、语音识别、数据挖掘等工程领域的广泛应用和切换系统在控制工程中的重要应用,切换神经网络模型的动力学问题引起了学术界的广泛关注。在研究切换神经网络的控制问题时,一般假设控制器和子系统切换是完全匹配的,即二者在切换律下同步运行,我们把它称为同步切换系统。然而,在实际工程的一些复杂大系统中,识别运行的子系统和确定匹配的控制器需要耗费一定的时间,那么控制器切换可能会滞后相应子系统切换,从而出现异步切换的现象。因此,研究同步和异步切换问题是十分必要和重要的。本文利用Lyapunov-Krasovskii泛函方法,平均驻留时间(ADT)方法以及线性矩阵不等式(LMI)方法结合随机分析方法和推广的詹森不等式技巧等方法,研究了切换Cohen-Grossberg神经网络模型的动力学行为。本文主要研究内容如下：针对具有切换的时滞Cohen-Grossberg神经网络模型,放弃大多数文献要求系统具有唯一平衡点的假设,利用时滞依赖的条件和线性矩阵不等式方法,获得了在平均驻留时间切换下系统的一致最终有界性、吸引子的存在性、全局指数稳定性与时滞依赖的判别条件。另外,通过一个数值例子验证了得出结果的有效性。研究了具有无界分布时滞及不确定性的切换随机Cohen-Grossberg神经网络模型,在范数有界的参数不确定性和白噪声干扰的情形下,利用随机分析方法,伊藤微分公式,线性矩阵不等式和平均驻留时间方法,得到了切换随机Cohen-Grossberg神经网络的随机一致最终有界、随机吸引子的存在性、均方指数稳定性成立的一系列充分条件。最后,运用Matlab进行了实例说明和数值模拟。分析了异步切换和变化时滞的随机Cohen-Grossberg神经网络模型的渐进行为,利用推广的二重时滞依赖的积分不等式,得到了新的时滞依赖的条件。通过分析匹配时间段和不匹配时间段,通过采用线性矩阵不等式和平均驻留时间方法以及伊藤微分公式保证了异步切换随机Cohen-Grossberg神经网络在平均驻留时间切换下的有界性、吸引子存在性、稳定性等一系列与变化时滞相关的新准则。最终数值模拟的结果和我们的理论相一致。更多还原

【Abstract】 In recent years, owing to the wide range of potential applications of neural networks both Engineering areas such as pattern recognition, Intelligent Computing, associate memory, Phoneme recognition, knowledge acquisition and the important applications of switched systems, the dynamical issues of switched neural networks have attracted worldwide attention in academics.For the control problem of switched neural networks, it is generally assumed that the switching of the controllers is matched with that of the subsystems, i.e., they are ac-tivated synchronously at switching ruler, we may be regards as synchronously switched systems. However, Some of the complex large systems in practical engineering, since it inevitably takes some time to identify the active subsystem and apply for the matched controller, the switching time of controllers may lag behind that of the correspond-ing subsystems, which leads to asynchronous switching. Therefor, it is necessary and important to investigate the issues of synchronously and asynchronously switching.Studying the problem of dynamics of switched Cohen-Grossberg neural networks(C-GNN) by using Lyapunov functional method, average dwell time (ADT), Linear ma-trix inequalities (LMIs) technique, stochastic analysis technology and extend Jensen inequalities. The main of contents of this paper as following:For delay-dependent switched Cohen-Grossberg neural networks. In previous lit-erature, giving up the assumes of the majority of existing literatures, which the systems have unique equilibrium point. Employ the condition of delay-dependent and Linear matrix inequalities. Some judging criterions on the uniformly ultimate boundedness, the existence of an attractors, the globally exponential stability of systems are devel-oped with ADT, which is closely related to delays. A numerical example is provided to illustrate the effectiveness of the proposed results.The uncertainty switched stochastic Cohen-Grossberg neural networks(SSCGNN) with bounded distributed delays is investigated. Under norm-bounded-parameter un-certainty and noise fluctuations, utilizing tochastic analysis technology, Ito differential formula, LMIs technique and ADT method. A series of sufficient conditions are ob-tained to ensue the stochastic uniformly ultimate boundedness, the existence of an stochastic attractor, and the globally exponential stability in the mean square of SS-CGNN. Eventually, examples illustrate and numerical simulation are carried out by Matlab.The asymptotic behaviors for SSCGNN. under asynchronous switching and vari-eties delays is investigated. The novel sufficient conditions are developed by extending double delay-dependent integral inequality. By dealing with matched and mismatched periods and using LMIs technique, ADT method and Ito differential formula, it make the boundedness, the existence of an attractor, and stability for SSCGNN under asyn-chronous with ADT are guaranteed. At last, numerical simulations show than the the-oretically predicted results are in excellent agreement with the numerically observed behavior.更多还原