多层异质复杂网络系统的能控性  

Controllability of Multi-layer Heterogeneous Complex Network Systems

作　　者：曹连谦 王立夫 孔芝 郭戈 CAO Lian-Qian;WANG Li-Fu;KONG Zhi;GUO Ge(School of Control Engineering,Northeastern University at Qinhuangdao,Qinhuangdao 066004)

机构地区：[1]东北大学秦皇岛分校控制工程学院,秦皇岛066004

出　　处：《自动化学报》2024年第11期2140-2153,共14页Acta Automatica Sinica

基　　金：国家自然科学基金(61573077,U1808205);中央高校基本科研业务费专项基金(N2023022)资助。

摘　　要：研究了节点状态为高维的多层复杂网络系统的能控性问题.讨论了节点的异质性、层间耦合和层内耦合对网络能控性的影响.研究发现当节点状态由同质变为异质、内耦合矩阵由相同变为不同时,对网络能控性均有影响(网络可以由能控变为不能控,反之亦然).对层间耦合模式为驱动响应模式和相互依赖模式,分别给出了网络系统能控的充分条件或必要条件.相比于直接应用经典的能控性判据,这些条件更易于验证,且驱动响应模式比相互依赖模式实现系统完全能控所需的条件更弱.This paper studies the controllability of multi-layer complex network systems with high-dimensional node states.We discuss the influence of node heterogeneity,inter-layer coupling,and intra-layer coupling on the controllability of the network.It is found that when the state of the node changes from homogeneous to heterogeneous or the inner-coupling matrix changes from identical to nonidentical,both have an impact on the controllability of the network(the network can be changed from controllable to uncontrollable,and vice versa).The sufficient or necessary conditions for the controllability of the networked system when the inter-layer coupling mode is the drive response mode and the interdependence mode are given,respectively.These conditions are easier to verify than using the classic controllability criteria directly,and the conditions that the drive response mode to achieve fully controllability are weaker than the conditions for the interdependence mode.

关 键 词：网络能控性 异质网络 多层网络 内耦合矩阵 

分 类 号：O157.5[理学—数学]