基于等势节点的能控图的构造  

he Construction of Controllable Graphs Based on Equipotential Nodes

作　　者：刘萌萌 纪志坚 刘允刚[3] 林崇[1,2] LIU Mengmeng;JI Zhijian;LIU Yungang;LIN Chong(Insitute of Complexity Science,College of Automation,Qingdao University,Qingdao 266071;Shandong Key Laboratory of Industrial Control Technology,Qingdao University,Qingdao 266071;School of Control Science and Engineering,Shandong University,Jinan 250061)

机构地区：[1]青岛大学自动化学院复杂性科学研究所,青岛266071 [2]青岛大学山东省工业控制技术重点实验室,青岛266071 [3]山东大学控制科学与工程学院,济南250061

出　　处：《系统科学与数学》2023年第12期3081-3094,共14页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(62033007,61873136);山东省泰山学者攀登计划;山东省泰山学者特聘教授人才支持计划(ts20190930)资助课题

摘　　要：文章研究了基于等势节点的多智能体系统的能控性,并提出了一种构造能控图的方法.首先,分析了拉普拉斯矩阵的特征值与多信号输入下的多智能体系统能控性之间的关系.其次,发现了单信号输入系统与多信号输入系统的能控性存在差异,结果表明多信号输入比单信号输入更容易实现系统的能控性.另外,研究了含有等势节点的拓扑结构与拉普拉斯矩阵的特征向量之间的关系,并提出了确保系统能控的领导者选择方法.随后,得到了多信号输入下基于等势节点的能控图的构造方法,给出了系统能控性的充要条件.最后,通过数值算例验证了构造方法的有效性.This paper studies the controllability of the multi-agent systems based on equipotential nodes,and proposes a method of constructing controllable graphs.Firstly,the relationship between the eigenvalues of the Laplacian matrix and the controllability of the multi-agent system with multi-signal inputs is provided.Secondly,it is found that there are differences between the controllability of the system with single-signal input and that of the system with multi-signal input.It is easier to realize the controllability of the system with multi-signal inputs than the case with single-signal input.In addition,the relationship between the topological structures with equipotential nodes and the eigenvectors of Laplacian matrix is provided,and a leader selection method is proposed to ensure controllability.Then,we analyze how to construct controllable graphs based on equipotential nodes for the multi-signal inputs system,and present a necessary and sufficient condition for controllability.Finally,a numerical example is given to verify the effectiveness of the method of constructing controllable graphs.

关 键 词：能控性 多智能体系统 能控子空间 领导者选择方法 等势节点 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]