基于0/-1特征值的网络可控性优化研究

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Title:

Optimizing network controllability based on eigenvalue 0/-1

作者:

陈兴凯¹, 卢昱¹, 王凯², 杨文兵³

1. 陆军工程大学 装备指挥与管理系, 河北 石家庄 050003;
2. 陆军工程大学 装备模拟训练中心, 河北 石家庄 050003;
3. 9804厂军代室, 云南 曲靖 655000

Author(s):

CHEN Xingkai¹, LU Yu¹, WANG Kai², YANG Wenbing³

1. Equipment Command and Management Department, Army Engineering University, Shijiazhuang 050003, China;
2. Equipment Simulation Training Center, Army Engineering University, Shijiazhuang 050003, China;
3. 9804 Military Representative Office, Qujing

关键词:

网络可控性; 最小控制输入; 特征值; 特征结构; 结构优化

Keywords:

network controllability; minimum control input; eigenvalue; feature structure; structure optimization

分类号:

TP273

DOI:

10.11992/tis.201801007

摘要:

针对网络可控性的优化问题，本文以PBH判据为基础，介绍了最小控制输入的求解方法以及网络可控性的定量分析指标；对λ_k I-A矩阵的行相关情况进行分类，明确了0/-1特征值与行重复相关、λ_k I-A矩阵行相关性的关系；阐述了0和-1特征值对应的独立共连和互连共连两种具有规律性的特征结构，以消除这两种结构为基本思路，给出了结构优化的基本步骤。通过实验分析，验证了0/-1特征值能够极大地影响网络的可控性，结构优化能够提高网络的可控性。研究结果表明：0/-1特征值具有重要性和可控性优化的有效性，可以为可控性的相关研究提供新方法、新思路。

Abstract:

Optimizing network controllability continues to be a research hotspot in network science. Based on the PBH criterion, in this paper, we introduce the computation method of minimum control input and the quantitative analysis index of network controllability. We classify the row correlations of the matrix λ_kI-A and confirm the relationship between eigenvalue 0/-1 and the row repetition correlation as well as the row correlation of matrix λ_kI-A. We describe two kinds of 0/-1 regularity structures, isolated and connected link structures. Using the method for eliminating these two kinds of regularity structures, we then propose the basic step of structure optimization. Through experimental analysis, we verify that the eigenvalue 0/-1 could greatly influence network controllability, and that structural optimization could improve network controllability. These results not only demonstrate the importance of eigenvalue 0/-1 and the effectiveness of optimizing controllability, but also provide a new method and concept for network controllability research.