复杂网络在路形拓扑结构下可控的充要条件  

Necessary and sufficient conditions for the controllability of complex networks with path topology

作　　者：晁永翠 纪志坚[1] 王耀威[1] 董洁[1] 

机构地区：[1]青岛大学自动化工程学院,山东青岛266071

出　　处：《智能系统学报》2015年第4期577-582,共6页CAAI Transactions on Intelligent Systems

基　　金：国家自然科学基金资助项目(61374062);山东省杰出青年科学基金资助项目(JQ201419)

摘　　要：分析了在路形拓扑结构下复杂网络的可控性问题。把系统的邻接矩阵进行适当分解,找到邻接矩阵的各子矩阵之间在特征值和特征向量上的关系,进而基于PBH(Popov-Belevitch-Hautus)判据,得到了复杂网络在路形拓扑结构下系统可控的充要条件。特别地,当控制节点为任意的某一个或多个节点时,给出了路图可控的判别方法。此外,文中提出了不可控特征值的概念,并给出了相应特征值的具体表达形式。文中2个主要定理通过算例进行验证,算例结果与定理结论一致。The controllability of complex networks is analyzed in the paper for path topology. With adjacency matrix of the system being decomposed into submatrices,the relationship between eigenvalues and eigenvectors is revealed for the partitioned submatrices. Furthermore,necessary and sufficient conditions are derived by taking advantage of the PBH（ Popov-Belevitch-Hautus） criteria. In particular,a method is proposed to determine path controllability when the controlled nodes are any single or multiple nodes,as well as the concept of uncontrollable eigenvalues is presented. The expressions for uncontrollable eigenvalues are provided as well. Two theorems in this paper is verified by examples and the results of examples are in agreement with the conclusion of the theorems.

关 键 词：复杂网络 可控性 图论 拓扑 线性定常系统 特征值 特征向量 控制系统 

分 类 号：O157.5[理学—数学]