三种胞腔划分下对多智能体系统能控性分析  

Controllability of Multi-Agent Systems Under Three Types of Partitions

作　　者：陈明彪 纪志坚[1] 渠继军 CHEN Mingbiao;JI Zhijian;QU Jijun(School of Automation,Qingdao University,Qingdao 266071,China)

机构地区：[1]青岛大学自动化学院,山东青岛266071

出　　处：《青岛大学学报(工程技术版)》2025年第1期1-8,16,共9页Journal of Qingdao University(Engineering & Technology Edition)

基　　金：国家自然科学基金项目(62373205;62033007);山东省泰山学者项目(tstp20230624;ts20190930);山东省泰山学者攀登计划及青岛大学系统科学+联合研究计划(XT2024101)。

摘　　要：基于距离划分、阶层划分和等价划分三种胞腔划分方法,研究了不同划分方式对多智能体系统能控子空间维数的影响。首先,结合距离划分和矩阵理论,给出了拓扑结构的直径与拉普拉斯矩阵特征值数量之间的关系。其次,利用阶层划分和等价划分,得到了系统能控子空间维数的下界,在此基础上,确定了领导者的选择与能控子空间维数之间的关系,证明了能控子空间的维数大于连通矩阵的秩与阶层节点数量之和。最后,当胞腔完全连通时,明确了输入向量的非零元素与能控子空间维数的关系。The dimension of the controllable subspace of systems is analyzed based on different cell partition methods.Initially,by integrating distance partition and matrix theory,the relationship between the diameter of the topological structure and the number of eigenvalues of the Laplacian matrix is derived.Subsequently,using hierarchical partition and equitable partition,the lower bound of the dimension of controllable subspace is determined.By this way,the relationship between the leaders selection and the dimension of the controllable subspace is analyzed,revealing that the dimension of the controllable subspace exceeds the sum of the rank of the connectivity matrix and the number of hierarchical nodes.Finally,when cells are fully connected,the relationship between the non-zero elements of the input vector and the dimension of the controllable subspace is clarified.

关 键 词：阶层划分 等价划分 能控子空间 连通分量 

分 类 号：TP273.5[自动化与计算机技术—检测技术与自动化装置] TN03[自动化与计算机技术—控制科学与工程]