几类复杂网络的同步及一致性研究

发布时间：2018-04-29 12:30

本文选题：指数同步 + QUAD条件　；参考：《武汉大学》2017年博士论文

【摘要】：在人类社会生活中,随着社会信息化的高速发展,复杂网络与我们的生活息息相关,复杂网络的研究不仅具有深刻的理论意义也具有广泛的实际应用价值.复杂网络的动力学行为是网络科学中重要的研究内容,它是网络的拓扑结构和微分方程相互交叉的研究领域,因此具有重要的理论意义和应用价值.同步和一致做为复杂网络中最典型的动力学现象,同步和一致在众多的学科领域以及工程应用中都具有广泛的应用前景.在复杂网络的同步和一致性研究中,为了研究的方便,研究者往往会对个体的动力学以及网络拓扑结构给予各种假设,而实际中的复杂网络系统中的个体的动力学以及网络拓扑结构却复杂得多,复杂网络的同步和一致研究中还有很多待解决的问题.在前人的研究基础上,利用图论、矩阵理论以及动力系统理论,本文进一步研究了复杂网络中的同步和一致性问题,其中在同步研究的部分,本文改进了个体动力学的假设条件,在一致性的研究部分,一方面考虑网络拓扑结构更复杂的系统,另一方面考虑个体动力学方程为分数阶的系统.具体的,本文一共分为六章,其中第一,二章简要的叙述了复杂网络的同步及一致性的研究背景和现状,以及介绍了一些与研究内容相关的预备知识,第三到五章为本文的研究工作,最后,在第六章对本文的研究内容进行总结并对未来的研究工作进行展望.本文的主要研究内容如下.1.在第三章中研究了个体自身的非线性动力学不需要满足QUAD条件或者弱的QUAD条件的线性耦合动力系统的指数同步问题,提出了两类更弱的动力学条件,给出此时关于系统实现同步的定理及推论,并在数值仿真中将本文的同步理论用于Hopfield神经网络,说明了本文理论的有效性和正确性.2.在第四章中给出了具有连续时间动态改变的拓扑结构的多智能体系统的有限时间协议,其中为了简化研究我们只考虑拓扑是无向的情况,应用图论、有限时间稳定理论,得到了系统实现局部有限时间一致和全局有限时间一致的条件,接下来也对系统实现有限时间一致的最短时间进行了估计,给出其满足的不等式条件,此外,我们也理论的证明了本章所给的有限时间一致性协议同样也适用于多智能体系统拓扑结构为固定或切换时的情况,最后数值仿真的实例也说明了这些结论的正确性.3.随着分数阶微积分的发展,许多自然界中的现象用具有分数阶动力学行为的系统可以得到很好的解释,同时在许多工程系统中,与整数阶模型相比,分数阶微分模型往往能更准确地模拟系统动力学过程,因此本文在第五章中研究了具有有向拓扑结构的分数阶多智能体系统在非线性协议下的一致问题,应用图论、矩阵理论和分数阶微积分的性质,给出非线性协议下分数阶多智能体实现一致的条件并给出了文中系统的一致值的具体表达式,同时给出具体的仿真实例,说明了分数阶多智能体在非线性协议下的一些特征,并与现有线性协议的结果进行比较.
[Abstract]:In human social life, with the rapid development of social information, complex networks are closely related to our lives. The study of complex networks not only has profound theoretical significance but also has extensive practical application value. The dynamic behavior of complex networks is the important research content of network science, it is the topology structure and micro network of network. It has important theoretical significance and application value. Synchronization and consistency are the most typical dynamic phenomena in complex networks. Synchronization and consistency have wide application prospects in many subject fields and engineering applications. In the study of synchronization and consistency of complex networks, for research It is convenient for researchers to give various assumptions about the dynamics of individual and network topology, and the dynamics of individual and network topology in the complex network system are much more complex. There are many problems to be solved in the synchronization and consistent research of complex networks. Based on previous studies, the graph theory is used. The problem of synchronization and consistency in complex networks is further studied by matrix theory and dynamic system theory. In the part of synchronization research, this paper improves the hypothesis of individual dynamics, in the research part of consistency, on the one hand, considering the more complex system of network topology, and on the other hand, the individual dynamics side is considered. This paper is divided into six chapters. In this paper, this paper is divided into six chapters. The first, second chapters briefly describe the background and status of the research on the synchronization and consistency of the complex network, and introduce some preparatory knowledge related to the research content. The third to five chapters are the research work of this paper. Finally, in the sixth chapter, the research content of this paper is introduced. The main research contents of this paper are as follows: in the third chapter,.1. studies the exponential synchronization problem of linear coupled dynamic systems that do not have to satisfy the QUAD condition or weak QUAD condition in the nonlinear dynamics of individual itself. The two kinds of weaker dynamic conditions are proposed, and the system is given at this time. The theorem and inference of synchronization are realized, and the synchronization theory of this paper is applied to the Hopfield neural network in numerical simulation, and the validity and correctness of this theory is illustrated by.2.. In the fourth chapter, the limited time protocol of a multi-agent system with a continuous time dynamic topology is given. In order to simplify the study we only Considering the fact that topology is undirected, using graph theory and finite time stability theory, the conditions for the system to achieve local finite time consistency and global finite time consistency are obtained. Then, the shortest time time consistency of the system is estimated, and the inequality conditions are given. In addition, we also prove this theory. The finite time conformance protocol given by the chapter also applies to the condition that the topology of the multi-agent system is fixed or switched. Finally, the example of numerical simulation also shows the correctness of these conclusions.3., with the development of fractional calculus, many natural phenomena which have fractional order dynamic behavior can be obtained. It is well explained that in many engineering systems, compared with the integer order model, the fractional order differential model can more accurately simulate the dynamic process of the system. Therefore, in the fifth chapter, the uniform problem of the fractional order multi-agent system with a directional topology is discussed, the application graph theory, the matrix theory and the theory of the matrix are applied. The properties of fractional calculus are given, the conditions for achieving the consistency of the fractional order multiagent under the nonlinear protocol are given and the concrete expression of the uniform value of the system is given. At the same time, a specific simulation example is given, and some characteristics of the fractional order multi-agent under the nonlinear protocol are illustrated, and the results are compared with the results of the existing linear protocols.

【学位授予单位】：武汉大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：O157.5

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