基于三种控制器的有色复杂网络的同步问题研究

发布时间：2018-11-17 13:03

【摘要】：自然界中存在各色各样的复杂网络,并且许多复杂网络都是由大规模的个体组成的。因此,近年来关于复杂网络的研究一直是学者们关注的热点。众所周知,一个大规模网络的动力学复杂性与个体间错综复杂的相互作用网络的耦合结构有关。但是外耦合结构矩阵描述的仅仅是个体之间是否存在相互作用,内耦合结构矩阵才能表达出个体间是怎样的相互作用。如果复杂网络的内耦合结构矩阵是与个体相关的,那么就叫做有色复杂网络,这是本文研究的基础网络。同步是一种非常典型的复杂网络的群聚行为,它可以通过网络个体间的相互作用来达到。同步现象的研究不仅仅可以帮助人们更清楚和深刻的认识自然和世界,还有很多方面的应用。但在真实的网络世界里,不是所有的网络都能达到同步,那么通常需要引入控制器来优化网络同步的速率等方面。本文就主要从优化控制器的角度来研究有色复杂网络的同步问题,并考虑随机噪声对网络同步现象的影响。本文的主要工作包括：1.首先对本文的基础网络—有色复杂网络进行了简要的介绍,并对将要用到的预备知识进行了梳理。在对有色复杂网络进行同步问题分析时,先对特殊的有色边复杂网络进行分析。本文第三章对同步问题的研究主要集中在控制器的的控制时间优化方面。分别对连续时间中的牵制控制、离散时间中的间歇牵制控制和随机发生的牵制控制策略下的有色边复杂网络的同步问题进行了研究。运用李雅普诺夫稳定性理论和变形的QUAD条件进行同步理论分析,分别得到有色边复杂网络实现同步的条件。对三种控制策略分别进行MATLAB数值模拟验证。2.在第三章数值模拟的基础上,选择三者中较好的一种控制器模型。继续在网络模型中引入噪声随机干扰项来优化网络的模型,使其能更准确的刻画自然界。在这一章中运用伊藤—德布林公式和李雅普诺夫稳定性理论等进行同步分析,得到实现同步的理论依据。最后给出数值验证,分析噪声对网络同步的影响。3.将有色边复杂网络同步研究中控制器的策略引入到一般的有色复杂网络中。由于一般复杂网络模型中节点动力学行为的不同,将其与开环控制器联合使用来达到网络同步目标状态。
[Abstract]:There are a variety of complex networks in nature, and many complex networks are made up of large-scale individuals. Therefore, in recent years, the research on complex networks has been the focus of attention by scholars. It is well known that the dynamic complexity of a large-scale network is related to the coupling structure of a complex interaction network between individuals. However, the external coupling structure matrix describes only whether there is interaction between individuals, and the internal coupling structure matrix can express the interaction between individuals. If the inner coupling structure matrix of a complex network is individual dependent, then it is called a colored complex network, which is the basic network studied in this paper. Synchronization is a typical clustering behavior of complex networks, which can be achieved by the interaction between individuals. The study of synchronization can not only help people to understand nature and the world more deeply, but also has many applications. But in the real network world, not all networks can achieve synchronization, so we usually need to introduce controller to optimize the speed of network synchronization. In this paper, the synchronization problem of colored complex networks is studied from the point of view of optimal controller, and the influence of random noise on network synchronization is considered. The main work of this paper includes: 1. Firstly, this paper briefly introduces the basic network-colored complex network, and combs the preparatory knowledge to be used. When analyzing the synchronization problem of colored complex network, the special colored edge complex network is analyzed first. The third chapter focuses on the control time optimization of the controller. The synchronization problems of colored edge complex networks with continuous time, discrete time and random occurrence control are studied respectively. By using Lyapunov stability theory and the QUAD condition of deformation, the synchronization conditions of colored edge complex network are obtained. The three control strategies are verified by MATLAB numerical simulation. 2. On the basis of numerical simulation in chapter 3, a better controller model is selected. The noise random disturbance term is introduced into the network model to optimize the network model so that it can describe the nature more accurately. In this chapter, Itoch-DeBrin formula and Lyapunov stability theory are used to analyze synchronization, and the theoretical basis for realizing synchronization is obtained. Finally, numerical verification is given, and the effect of noise on network synchronization is analyzed. 3. 3. In this paper, the strategy of controller in the research of color-edge complex network synchronization is introduced into the general colored complex network. Because the dynamic behavior of nodes in general complex network model is different, it is combined with open-loop controller to achieve the target state of network synchronization.
【学位授予单位】：深圳大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O157.5;O231

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