基于拓扑结构和个体动态层面的多智能体系统可控性分析  

Controllability analysis of multi-agent systems based on topological structure and individual dynamic level

作　　者：陈万金 纪志坚[1] CHEN Wanjin;JI Zhijian(School of Automation Engineering,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：《智能系统学报》2020年第2期264-270,共7页CAAI Transactions on Intelligent Systems

基　　金：国家自然科学基金项目(61873136,61603288,61374062);山东省杰出青年科学基金项目(JQ201419)。

摘　　要：针对一般线性多智能体系统中网络拓扑及个体动态这两个层面的可控性对系统整体可控性的关系进行了研究,提出了一种新的描述一般线性多智能体系统的模型。利用PBH(Popov-Belevitch-Hautus)判据,得到并证明了在此模型下多智能体系统可控性在网络拓扑结构与个体动态层面的充要条件。结合具体的例子解释了系统矩阵中出现重复特征值时对定理2充分性的影响,并且提供了一种避免重复特征值出现的方法。特别地,推导出了此模型下系统矩阵为实对称矩阵这一特殊情况时可以判定该系统不可控的两种判定条件,即比较系统矩阵中最大的特征值代数重数与控制矩阵中1元素的个数,满足条件即判定系统不可控。The relationship between the controllability of network topology and individual dynamics in the overall controllability of the system is studied,and a new model describing the general linear multi-agent system is proposed.Using the Popov-Belevitch-Hautus(PBH)criterion,the necessary and sufficient conditions for the controllability of a multi-agent system in the network topology and individual dynamic level are obtained and proved,and the effect of repeated eigenvalues in the system matrix on the sufficiency of Theorem 2 is explained with a concrete example.We provide a way to avoid the occurrence of repeated eigenvalues.In particular,the two conditions for judging the uncontrollable system can be determined when the system matrix is a real symmetric matrix under this model;that is,compare the largest eigenvalue algebraic multiplicity in the system matrix with the number of 1 elements in the control matrix.If this condition is satisfied,the system is uncontrollable.

关 键 词：多智能体系统 可控性 线性定常系统 拓扑 邻居信息交互 特征值 特征向量 控制理论 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]