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多层异质复杂网络系统的能控性

曹连谦 王立夫 孔芝 郭戈

曹连谦, 王立夫, 孔芝, 郭戈. 多层异质复杂网络系统的能控性. 自动化学报, 2021, 48(x): 1−13 doi: 10.16383/j.aas.c210654
引用本文: 曹连谦, 王立夫, 孔芝, 郭戈. 多层异质复杂网络系统的能控性. 自动化学报, 2021, 48(x): 1−13 doi: 10.16383/j.aas.c210654
Cao Lian-Qian, Wang Li-Fu, Kong Zhi, Guo Ge. Controllability of multi-layer heterogeneous complex network systems. Acta Automatica Sinica, 2021, 48(x): 1−13 doi: 10.16383/j.aas.c210654
Citation: Cao Lian-Qian, Wang Li-Fu, Kong Zhi, Guo Ge. Controllability of multi-layer heterogeneous complex network systems. Acta Automatica Sinica, 2021, 48(x): 1−13 doi: 10.16383/j.aas.c210654

多层异质复杂网络系统的能控性

doi: 10.16383/j.aas.c210654
基金项目: 国家自然科学基金项目(61573077, U1808205), 中央高校基本科研业务费专项基金项目(N2023022)资助
详细信息
    作者简介:

    曹连谦:东北大学秦皇岛分校硕士研究生. 研究方向为复杂网络能控性. E-mail: caolianqian1@yeah.net

    王立夫:东北大学秦皇岛分校副教授. 研究方向为复杂网络, 同步控制, 能控性, 交通网络. 本文通信作者. E-mail: wlfkz@qq.com

    孔芝:东北大学秦皇岛分校副教授. 研究方向为知识发现, 决策分析, 智能优化算法, 复杂网络. E-mail: kongz@neuq.edu.cn

    郭戈:东北大学教授. 研究方向为智能交通系统, 交通大数据分析, 人工智能应用, 信息物理系统. E-mail: geguo@yeah.net

Controllability of Multi-Layer Heterogeneous Complex Network Systems

Funds: Supported by National Natural Science Foundation of China (61573077, U1808205), Fundamental Research Funds for the Central Universities (N2023022)
More Information
    Author Bio:

    CAO Lian-Qian Postgraduate student of Northeastern University at Qinhuangdao. His research interest is controllability of complex networks

    WANG Li-Fu Associate professor of Northeastern University at Qinhuangdao. His research interests include complex networks, synchron-ous control, controllability, and traffic networks. Corresponding author of this article

    KONG Zhi Associate professor of Northeastern University at Qinhuang-dao. Her research interests include knowledge discovery, decision analy-sis, intelligent optimization algorithms, and complex networks

    GUO Ge Professor of Northeastern University. His research interests include intelligent transportation systems, traffic big data analysis, artificial intelligence applications, and information physical systems

  • 摘要: 本文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、层内耦合对网络能控性的影响. 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, 对网络能控性均有影响(网络既可由能控变为不能控, 又可由不能控变为能控); 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.
  • 图  1  层间耦合为驱动响应模式的两层网络

    Fig.  1  Two-layer networks with the inter-layer drive-response couplings

    图  2  层间耦合为相互依赖模式的两层网络

    Fig.  2  Two-layer networks with the inter-layer interdependent couplings

    图  3  层间耦合为驱动响应模式的M层网络结构

    Fig.  3  The illustration of three-layer networks with the inter-layer interdependent couplings

    图  4  层间耦合为相互依赖模式的3层网络示意图

    Fig.  4  The illustration of three-layer networks with the inter-layer interdependent couplings

    图  5  驱动层为链网络响应层为星形网络的两层网络

    Fig.  5  Two-layer networks with the topology of the drive-layer is a chain network, and the response layer is a star network.

    表    附录A 本文模型中所用的特殊记号

    Table    Appendix A. Special notations used in the model of this paper

    特殊记号含义
    $ A_i^K $第$ K $层网络的第$ i $个节点的状态矩阵
    $ B_i^K $第$ K $层网络的第$ i $个节点的输入矩阵
    $ C_i^K $第$ K $层网络的第$ i $个节点的输出矩阵
    $ H_i^K $第$ K $层网络的第$ i $个节点与该层其他节点之间的内耦合矩阵
    $ H_i^{KJ} $第$ J $层网络的第$ i $个节点与第$ K $层网络的其他节点之间的内耦合矩阵
    $ {W^K} $第$ K $层的网络拓扑
    $ {D^{KJ}} $第$ J $层到第$ K $层的网络拓扑
    $ x $整个网络系统的状态
    $ {x^K} $第$ K $层网络的状态
    $ u $整个网络系统的输入
    $ {u^K} $第$ K $层网络的输入
    $ \Phi $整个网络系统的状态矩阵
    $ {\Phi _{KK}} $第$ K $层网络的状态矩阵
    $ {\Phi _{KJ}} $第$ J $层到第$ K $层网络的状态矩阵
    $ \Psi $整个网络系统的输入矩阵
    $ \Xi $整个网络系统的输出矩阵
    $ {\Lambda ^K} $以$A_1^K,\cdots,A_N^K$为对角元的分块对角矩阵
    $ \Delta $对角矩阵${ {\text{diag} } } \{ {\Delta ^1},\cdots,{\Delta ^M}\}$
    $ {\Delta ^K} $对角矩阵${ {\text{diag} } } \{ \delta _1^K,\cdots,\delta _N^K\}$
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  • 收稿日期:  2021-07-14
  • 修回日期:  2021-12-14
  • 网络出版日期:  2022-02-04

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