控制理论与应用2022，Vol.39Issue(10)：1799-1806,8.DOI:10.7641/CTA.2022.10838
含生成森林有向图的零特征值及在编队控制中的应用
Zero eigenvalue of directed graphs with spanning forests with application to formation control
摘要
Abstract
This paper investigates the multiplicity of zero eigenvalue of the Laplacian matrix for a directed graph,which has a spanning m-forest,where m≥1 is an integer.For this problem,the graph usually does not contain a spanning tree,and this scenario may occur due to insidious attacks or communication blocking by obstacles between two agents in distributed control,(online)optimization,multi-agent operators,and so on,even though it indeed has a spanning tree at the beginning.In addition,this problem is of interest as a research direction in its own right.To deal with this problem,it is shown that the multiplicity of the Laplacian's zero eigenvalue amounts to the number of spanning forests in the studied graph,which can be seen as an extension of the directed graph case with a spanning tree,in which case it has m=1.Moreover,the obtained result is applied to formation control for single-integrator multi-agent systems along with distributed optimization methods,indicating that the achieved formation shape lies in the kernel space of the Laplacian matrix associated with the communication graph.Finally,an example is provided to demonstrate the applicability to formation control.关键词
拉普拉斯矩阵/多智能体网络/有向图/生成森林/编队控制Key words
Laplacian matrix/multi-agent networks/directed graphs/spanning forest/formation control引用本文复制引用
李修贤,李莉,谢立华..含生成森林有向图的零特征值及在编队控制中的应用[J].控制理论与应用,2022,39(10):1799-1806,8.基金项目
Supported by the National Natural Science Foundation of China(62003243,72171172),the Fundamental Research Funds for the Central U-niversities(22120210099),the Shanghai Municipal Commission of Science and Technology(19511132101),the Shanghai Municipal Science and Technology Major Project(2021SHZDZX0100)and the Basic Science Centre Program by National Natural Science Foundation of China(62088101). （62003243,72171172）
