有向网络下线性多个体系统的整体行为--矩阵方法  

Collective behavior of linear multi-agent system in directed network:A matrix approach

作　　者：金继东[1,2] 郑毓蕃[1] 

机构地区：[1]上海大学数学系,上海200444 [2]首都经济贸易大学计算机科学与技术系,北京100070

出　　处：《控制与决策》2011年第5期661-666,共6页Control and Decision

基　　金：国家自然科学基金项目(60674046)

摘　　要：研究了有向通讯网络条件下一阶和二阶线性多个体协同动力学系统整体行为的矩阵代数性质.利用矩阵分析的方法将系统的系数矩阵变换为Frobenius标准型,由此将系统分解为独立基本子系统和非独立基本子系统的组成结构.通过研究行和为零的对角占优矩阵的性质,得出了对线性多个体协同动力学系统整体行为起决定作用的系数矩阵的性质,从而将这一问题转换为普通线性代数问题.This paper studies the matrix algebra properties of the collective behavior of liner multi-agent dynamic systems in directed network,where the agent is with dynamical order one or two.By means of matrix analysis approach,the coefficient matrix of system can be transformed into Frobenius canonical form.Thus,the system is decomposed into several basic independent subsystems and basic non-independent subsystems.Based on the study of diagonally dominant matrices with the sum of entries in each row being zero,some properties of coefficient matrix are obtained,which play a key role in the collective behavior of liner multi-agent dynamic systems.Thus,the study of collective behavior of system is reduced to some elementary linear algebra problems.

关 键 词：Frobenius标准型 对角占优 惯性 带权中心 凸组合 

分 类 号：N941.3[自然科学总论—系统科学] O231.5[理学—运筹学与控制论]