大规模有向网络的K可控性研究  

Research on K-controllability of large-scale directed networks

作　　者：曾涛 李晓丽 ZENG Tao;LI Xiaoli(College of Information Science and Technology,Ministry of Education,Donghua University,Shanghai 201620,China;Engineering Research Center of Digitalized Textile and Fashion Technology,Ministry of Education,Donghua University,Shanghai 201620,China)

机构地区：[1]东华大学信息科学与技术学院,上海201620 [2]东华大学数字化纺织服装技术教育部工程研究中心,上海201620

出　　处：《东华大学学报（自然科学版）》2023年第2期121-127,135,共8页Journal of Donghua University(Natural Science)

基　　金：上海市自然科学基金资助项目(16ZR1446700);上海市浦江人才计划资助项目(18PJ1400100);中央高校基本科研业务费专项基金资助项目(20D110425)。

摘　　要：为研究大规模有向网络系统的控制性能,采用结构能控性指数K来表征网络系统的控制长度。提出K可控定理,将有向网络系统分解成独立可控的“仙人掌”结构,得出系统可控时的驱动节点集和结构能控性指数K。提出大规模网络系统矩阵的K可控算法,将K可控定理在算法中实现,并对大规模随机网络和真实网络进行仿真。结果表明,利用K可控定理可以得出大规模有向网络系统的结构能控性指数K。讨论结构能控性指数K和最小控制输入之间的关系。In order to analyze the control performance of large-scale directed network system,the structural controllability index K is used to characterize the control length of network system.The Kcontrollability theorem is proposed to decompose the directed network system into independent controllable“cactus”structure,and the driving node set and structure controllability index K are obtained when the system is controllable.The K-controllability algorithm of large-scale network system matrix is proposed,and the K-controllability theorem is realized in the algorithm.The simulation of large-scale random network and real network is carried out.The results show that the structural controllability index K of large-scale directed network system can be obtained by using the Kcontrollability theorem.The relationship between the structural controllability index K and the minimum control input is discussed.

关 键 词：K可控定理 大规模网络 驱动节点集 能控性指数 

分 类 号：O231.1[理学—运筹学与控制论]