有向路径下的一类多智能体系统的能控性分析  

Controllability of Multi-agent System Based on Directed Paths

作　　者：张志伟 纪志坚[1,2] ZHANG Zhiwei;JI Zhijian(School of Automation,Qingdao University,Qingdao 266071,China;Shandong Key Laboratory of Industrial Control Technology,Qingdao University,Qingdao 266071,China)

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

出　　处：《复杂系统与复杂性科学》2022年第2期63-70,95,共9页Complex Systems and Complexity Science

基　　金：国家自然科学基金(61873136,62033007);山东省泰山学者攀登计划和山东省泰山学者支持计划(ts20190930)。

摘　　要：为研究一类基于有向路径下的有向符号多智能体系统的能控性,利用Laplacian矩阵和图理论知识进行了分析。首先证明了增加或删除网络中特定的一类边对于系统的能控性没有影响。其次,对有向路径以及路径中增加逆向边和顺向边后系统的能控性进行了研究。结果表明:增加逆向边不改变系统能控性,而增加顺向边时系统能控性需要利用等价划分根据具体情况进行分析。最后,综合以上结果给出了一种构造复杂能控有向拓扑的方法。To study the controllability of a class of directed signed multi-agent systems based on directed paths,the Laplacian matrix and graph theory are used to analyze.Firstly,it is proved that adding or removing a specific class of edges in the network does not change the system′s controllability.Secondly,the controllability of the directed paths is studied,and then we check the system′s controllability after adding reverse or forward edges in the directed paths.The results show that increasing the reverse edges in directed paths has no influences on its original controllability,However,the system’s controllability needs to be analyzed according to the specific situations while increasing the forward ones by taking advantage of the almost equitable partitons.Finally,combined with the results above,a method of constructing directed complex network topologies is given.

关 键 词：leader-follower结构 多智能体系统 能控性 有向路径图 几乎等价划分 

分 类 号：TP273.5[自动化与计算机技术—检测技术与自动化装置]