定量参数和简单拓扑结构下的可控性

发布时间：2018-04-04 14:40

本文选题：多个体系统　切入点：条件数　出处：《青岛大学》2017年硕士论文

【摘要】：多个体系统的可控性是多个体系统研究中的一个基本而又重要的概念。本文的主要研究内容包括:本文概述了多个体系统可控性研究的背景和意义以及国内外发展的现状。针对多个体系统的可控性问题,把用于解决问题的图论、矩阵理论和线性系统理论的相关知识进行了总结。在多个体系统的一致性协议下,对系统的Laplacian矩阵进行分块,基于系统可控性判别矩阵的条件数,提出一个定量参数。该参数可以影响多个体系统可控性,然后基于该参数的值对多个体系统可控性进行分析。多个体系统的可控性与该参数的值相关,该参数的值不仅可以用来判别系统是否可控,还可以用来衡量一个多个体系统可控性的程度。最后通过实例进行说明。对多个体系统模型,复杂网络系统模型和关联网络系统模型进行了综述。并在相同的系统拓扑结构图(有向路图和有向树图)下,对这几种系统模型的可控性进行了研究,从而归纳出其可控性的共性。
[Abstract]:The controllability of multi-individual systems is a basic and important concept in the study of multi-individual systems.The main contents of this paper are as follows: this paper summarizes the background and significance of the research on the controllability of multi-individual systems and the current situation of its development at home and abroad.Aiming at the controllability problems of multi-individual systems, the relevant knowledge of graph theory, matrix theory and linear system theory for solving problems are summarized.Based on the condition number of the controllability discriminant matrix, a quantitative parameter is proposed by dividing the Laplacian matrix of the system into blocks under the consistency protocol of the multi-individual system.This parameter can affect the controllability of multi-individual system, and then analyze the controllability of multi-individual system based on the value of the parameter.The controllability of multi-individual system is related to the value of the parameter. The value of the parameter can be used not only to judge whether the system is controllable, but also to measure the degree of controllability of a multi-individual system.Finally, an example is given to illustrate the problem.The multi-individual system model, complex network system model and associated network system model are reviewed.Under the same system topology structure graph (directed path graph and directed tree graph), the controllability of these system models is studied, and the generality of their controllability is concluded.
【学位授予单位】：青岛大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5;O231

【参考文献】