矩阵权重下的多智能体边能控性  

Multi-Agent Edge Controllability Under Matrix Weights

作　　者：侯彩侠 纪志坚[1,2] HOU Caixia;JI Zhijian(School of Automation,Qingdao University,Qingdao 266071;Shandong Key Laboratory of Industrial Control Technology,Qingdao 266071)

机构地区：[1]青岛大学自动化学院,青岛266071 [2]山东省工业控制技术重点实验室,青岛266071

出　　处：《系统科学与数学》2024年第9期2549-2563,共15页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(62373205,62033007);山东省泰山学者特聘教授人才支持计划(tstp20230624,ts20190930);山东省泰山学者攀登计划资助课题。

摘　　要：文章借助拓扑图从点图到线图的转换,研究了矩阵权重下多智能体系统的边能控性,其中动态发生在边上.首先,从图论的角度对线图的关联矩阵进行了定量分析,给出了线图关联矩阵的秩与连通分量个数之间的关系,进一步得到线图拉普拉斯矩阵零特征值的代数重数与连通分量的个数也存在一定的联系.其次,在领导者-跟随者结构模型下,得到了多智能体系统边可控时需要满足的两个条件.此外,根据规范变换的定义,将矩阵权重结构平衡下的符号线图变换为不含负边的无符号线图.结果表明,变换前后线图的可控性是等价的.最后,分析了线图可控性与点图可控性之间的关系.得到当点图结构不平衡时,线图的可控性等同于点图的可控性.In this paper,the edge controllability of multi-agent systems under matrix weights is studied by using the transformation of topological graphs from point graphs to line graphs,where dynamics occur on the edges.Firstly,from the perspective of graph theory,a quantitative analysis is conducted on the incidence matrix of a line graph,and the relationship between the rank of the incidence matrix of the line graph and the number of connected components of the line graph are given.Furthermore,we find that there is a certain relationship between the algebraic multiplicity of zero eigenvalues of the Laplacian matrix of the line graph and the number of connected components of the line graph.Secondly,under the leader follower structure model,two conditions that need to be satisfied when the multi-agent system is edge controllable are obtained.In addition,according to the definition of canonical transformation,the balanced symbolic line graph of matrix weight structure is transformed into an unsigned line graph without negative edges.The results show that the controllability of the line graph before and after transformation is equivalent.Finally,the relationship between the controllability of line graphs and point graphs is analyzed,and it is found that when the point graph is structurally imbalanced,the controllability of line graphs is equivalent to that of point graphs.

关 键 词：多智能体系统 矩阵权重 线图 边可控性 符号网络 关联矩阵 

分 类 号：O231[理学—运筹学与控制论] TP18[理学—数学]