几类反应扩散神经网络的控制与同步

发布时间：2018-01-08 09:21

本文关键词：几类反应扩散神经网络的控制与同步　出处：《新疆大学》2017年硕士论文　论文类型：学位论文

【摘要】：反应扩散神经网络的控制与同步是当今神经网络动力学研究的热点问题之一,越来越受到国内外学者的广泛关注.本文通过设计不同的离散型控制器,分别研究了具有混合时滞的BAM反应扩散神经网络的牵制脉冲控制、具有时滞的混合耦合反应扩散神经网络的间歇采样同步以及具有切换拓扑的耦合反应扩散神经网络的自适应间歇同步.本文的主要工作概括如下:在第1节引言中,论述了反应扩散神经网络动力学的研究背景和研究现状,介绍了控制与同步反应扩散神经网络的常用方法,并提出了本文的研究内容.在第2节中,利用牵制脉冲控制,对具有混合时滞的BAM反应扩散神经网络进行了指数稳定化.在设计的控制器中,脉冲控制函数可以是非线性的,并且我们是依据系统状态误差在每一个脉冲点的重新排序来选取有哪些神经元将受到牵制.此外,基于所设计的控制器和Lyapunov函数,我们得到了一系列依赖于扩散系数和控制参数的网络全局指数稳定判别准则.最后,通过两个例子验证了理论结果的正确性.在第3节中,通过具有空间采样的间歇控制,研究了具有时滞的混合耦合反应扩散神经网络的指数同步问题,得到了一系列使得网络指数同步的充分条件,这些条件不但依赖于时滞和扩散系数,还依赖于网络的耦合强度.此外,本节中所运用的控制方法,不仅包含了周期和非周期两种间歇控制,而且,在沿时间方向进行间歇控制的同时,还沿空间方向进行了采样控制.在本节的最后,我们通过数值仿真实验验证了间歇采样控制的可行性和有效性.在第4节中,通过常增益间歇控制和自适应间歇控制,讨论了具有切换拓扑的耦合反应扩散神经网络的同步问题,得到了一系列依赖于扩散系数和网络耦合强度的网络同步判别准则.而在自适应间歇控制中,自适应控制增益不仅与时间有关,还与空间变量有关.最后,我们对本节的主要结果进行了数据模拟.
[Abstract]:The control and synchronization of reaction-diffusion neural networks (RNN) is one of the hot issues in the research of neural network dynamics, and has attracted more and more attention from scholars at home and abroad. In this paper, different discrete controllers are designed. In this paper, the control of BAM reaction-diffusion neural networks with mixed delay is studied. The intermittent sampling synchronization of a hybrid coupled reaction diffusion neural network with time delay and the adaptive intermittent synchronization of a coupled reaction-diffusion neural network with switching topology are presented. The main work of this paper is summarized as follows:. In the introduction to section 1. This paper discusses the research background and present situation of the dynamics of reactive diffusion neural networks, introduces the common methods of controlling and synchronizing the reaction diffusion neural networks, and puts forward the research contents of this paper. The BAM reaction-diffusion neural network with mixed time delay is exponentially stabilized by the choke pulse control. In the designed controller, the pulse control function can be nonlinear. And we select which neurons will be restrained according to the reordering of system state error at each pulse point. In addition, based on the designed controller and Lyapunov function. We obtain a series of global exponential stability criteria which depend on the diffusion coefficient and control parameters. Finally, two examples are given to verify the correctness of the theoretical results. By means of intermittent control with spatial sampling, the exponential synchronization problem of hybrid coupled reaction diffusion neural networks with time delay is studied, and a series of sufficient conditions for exponential synchronization of the networks are obtained. These conditions depend not only on the delay and diffusion coefficient, but also on the coupling strength of the network. In addition, the control methods used in this section include not only periodic and aperiodic intermittent control, but also. At the same time of intermittent control along the direction of time, sampling control is also carried out along the direction of space. At the end of this section. The feasibility and effectiveness of intermittent sampling control are verified by numerical simulation. In section 4, we use constant gain intermittent control and adaptive intermittent control. In this paper, the synchronization problem of coupled reactive diffusion neural networks with switching topology is discussed. A series of network synchronization criteria dependent on diffusion coefficient and network coupling strength are obtained, but in adaptive intermittent control. The adaptive control gain is not only related to time, but also to spatial variables. Finally, we simulate the main results of this section.
【学位授予单位】：新疆大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175;O231

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