[1]晁永翠,纪志坚,王耀威,等.复杂网络在路形拓扑结构下可控的充要条件[J].智能系统学报编辑部,2015,10(4):577-582.[doi:10.3969/j.issn.1673-4785.201411031]
CHAO Yongcui,JI Zhijian,WANG Yaowei,et al.Necessary and sufficient conditions for the controllability of complex networks with path topology[J].CAAI Transactions on Intelligent Systems,2015,10(4):577-582.[doi:10.3969/j.issn.1673-4785.201411031]
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CHAO Yongcui,JI Zhijian,WANG Yaowei,et al.Necessary and sufficient conditions for the controllability of complex networks with path topology[J].CAAI Transactions on Intelligent Systems,2015,10(4):577-582.[doi:10.3969/j.issn.1673-4785.201411031]
复杂网络在路形拓扑结构下可控的充要条件
《智能系统学报》编辑部[ISSN 1673-4785/CN 23-1538/TP] 卷:
10
期数:
2015年第4期
页码:
577-582
栏目:
学术论文—人工智能基础
出版日期:
2015-08-25
- Title:
- Necessary and sufficient conditions for the controllability of complex networks with path topology
- Keywords:
- complex networks; controllability; graph theory; topology; linear time-invariant systems; eigenvalue; eigenvectors; control system
- 分类号:
- TP18
- 文献标志码:
- A
- 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。
- Abstract:
- 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.
- 参考文献/References:
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备注/Memo
收稿日期:2014-11-25;改回日期:。
基金项目:国家自然科学基金资助项目(61374062).
作者简介:晁永翠,女,1990年生,硕士研究生,主要研究方向为复杂网络的可控性;纪志坚,男,1973年生,教授,博士生导师,博士,主要研究方向为群体系统动力学与协调控制、复杂网络、切换动力系统的分析与控制、系统生物以及基于网络的控制系统等。主持国家自然科学基金项目3项。发表学术论文70余篇,其中SCI收录23篇,EI收录50余篇;王耀威,男,1989年生,硕士研究生,主要研究方向为多智能体系统。
通讯作者:纪志坚.E-mail:jizhijian@pku.org.cn.
更新日期/Last Update:
2015-08-28