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复杂网络能控性鲁棒性研究进展

楼洋 李均利 李升 邓浩

楼洋, 李均利, 李升, 邓浩. 复杂网络能控性鲁棒性研究进展. 自动化学报, 2022, 48(10): 2374−2391 doi: 10.16383/j.aas.c200916
引用本文: 楼洋, 李均利, 李升, 邓浩. 复杂网络能控性鲁棒性研究进展. 自动化学报, 2022, 48(10): 2374−2391 doi: 10.16383/j.aas.c200916
Lou Yang, Li Jun-Li, Li Sheng, Deng Hao. Recent progress in controllability robustness of complex networks. Acta Automatica Sinica, 2022, 48(10): 2374−2391 doi: 10.16383/j.aas.c200916
Citation: Lou Yang, Li Jun-Li, Li Sheng, Deng Hao. Recent progress in controllability robustness of complex networks. Acta Automatica Sinica, 2022, 48(10): 2374−2391 doi: 10.16383/j.aas.c200916

复杂网络能控性鲁棒性研究进展

doi: 10.16383/j.aas.c200916
基金项目: 国家自然科学基金(62002249), 浙江大学CAD & CG国家重点实验室开放课题(A2112)资助
详细信息
    作者简介:

    楼洋:四川师范大学副研究员, 中国香港城市大学博士后. 2017年获得中国香港城市大学博士学位. 主要研究方向为复杂网络, 进化算法和机器学习. E-mail: felix.lou@my.cityu.edu.hk

    李均利:四川师范大学研究员. 2002年获得浙江大学博士学位. 主要研究方向为图像处理, 目标跟踪, 智能计算. 本文通信作者. E-mail: li.junli@vip.163.com

    李升:四川师范大学硕士研究生. 主要研究方向为复杂网络.E-mail: yunchunrui@163.com

    邓浩:四川师范大学硕士研究生. 主要研究方向为进化计算, 复杂网络.E-mail: 18108015390@189.cn

Recent Progress in Controllability Robustness of Complex Networks

Funds: Supported by National Natural Science Foundation of China (62002249) and the Open Project Program of the State Key Laboratory of CAD & CG, Zhejiang University (A2112)
More Information
    Author Bio:

    LOU Yang Associate professor at Sichuan Normal University and Postdoctoral Fellow at City University of Hong Kong, China. He received his Ph.D. degree from City University of Hong Kong, China in 2017. His research interest covers complex networks, evolutionary computation, and machine learning

    LI Jun-Li Professor at Sichuan Normal University. He received his Ph.D. degree from Zhejiang University in 2002. His research interest covers image processing, target tracking, and computational intelligence. Corresponding author of this paper

    LI Sheng Master student at Si-chuan Normal University. His research interest covers complex networks

    DENG Hao Master student at Sichuan Normal University. His research interest covers evolutionary computing and complex networks

  • 摘要: 研究复杂网络能控性鲁棒性对包括社会网络、生物和技术网络等在内的复杂系统的控制和应用具有重要价值. 复杂网络的能控性是指: 可通过若干控制节点和适当的输入, 在有限时间内将系统状态驱动至任意目标状态. 能控性鲁棒性则是指在受到攻击的情况下, 复杂网络依然维持能控性的能力. 设计具有优异能控性鲁棒性的复杂网络模型和优化实际网络的能控性鲁棒性一直是复杂网络领域的重要研究内容. 本文首先比较了常用的能控性鲁棒性定义及度量, 接着从攻击策略的角度分析了3类攻击的特点及效果, 包括随机攻击、基于特征的蓄意攻击和启发式攻击. 然后比较了常见模型网络的能控性鲁棒性. 介绍了常用优化策略, 包括模型设计和重新连边等. 目前的研究在攻击策略和拓扑结构优化方面都取得了进展, 也为进一步理论分析提供条件. 最后总结全文并提出潜在研究方向.
  • 图  1  匹配和节点控制中心性的例子

    Fig.  1  Examples of matching and node control centrality

    图  2  按文献[57]连边分类举例

    Fig.  2  An example of edge classification according to [57]

    图  3  按文献[57]节点分类举例

    Fig.  3  An example of node classification according to [57]

    图  4  能控性鲁棒性度量方式比较举例

    Fig.  4  Comparison of two different controllability robustness measurements

    图  5  能控性鲁棒性与连通性鲁棒性

    Fig.  5  Controllability robustness and connectedness robustness

    图  6  关键连边和关键节点在遭受攻击过程中变化

    Fig.  6  Critical edges and nodes may change during attacks

    图  7  常见的网络模型在攻击下的能控性曲线变化

    Fig.  7  The controllability curves of 9 network topologies under 4 different attack strategies

    图  8  所有$ N $节点和$ M $连边网络, 满足ENC的网络、全齐网络, 以及最优网络之间的关系图

    Fig.  8  The relationship diagram of the N-node M-edge networks, ENC networks, totally homogeneous networks, and the optimal networks

    表  1  常用能控性鲁棒性优化策略的优点与不足

    Table  1  Pros and cons of the strategies for controllability robustness optimization

    优化策略优点不足
    模型优化设计基于特定理论, 模型简单易实现
    (如同余论[122]、Henneberg[106] 理论)
    容易受理论约束 (如同余论限制生成网络的度数不能任意调整)
    重新连边根据实际需求, 对网络结构做一定范围的调整具有一定的随机性, 且通常需要较大的计算量
    全齐网络经验上的能控性鲁棒性最优结构通常不符合实际网络特征与需求 (如交通网络无法设计为全齐网络)
    模体在优化设计或重新连边过程中, 刻意增加网络中特定模体的数量不同模体对能控性鲁棒性的理论价值和意义有待进一步理清
    下载: 导出CSV

    表  2  能控性鲁棒性优化的网络结构

    Table  2  Comparison of network topologies with optimized controllability robustness

    网络结构优化设计重新连边全齐网络模体
    MCN
    QSN
    QSNR
    RTN
    RRN
    EH
    下载: 导出CSV
    $ A $邻接矩阵
    $ {A}_{ij} $邻接矩阵中节点$ i $和$ j $之间的连边
    $ {b}_{i} $节点$ i $的介数
    $ B $输入矩阵
    $ C $能控性矩阵
    $ {\cal{E}} $网络连边集合
    $ G $复杂网络
    $ {k}_{i} $节点$ i $的度数
    $ {k}_{i}^{{\rm{out}}} $节点$ i $的出度
    $ {k}_{i}^{{\rm{in}}} $节点$ i $的入度
    $ M $网络连边数
    $ {M}_{c} $关键连边数
    $ {M}_{r} $当前已攻击的连边数
    $ N $网络节点数
    $ {N}_{D} $网络所需控制节点数
    $ \Delta {N}_{D} $网络所需控制节点数增量
    $ {N}_{r} $当前已攻击的节点数
    $ {n}_{D} $网络所需控制节点密度
    $ p\left({M}_{c}\right) $关键连边比例
    $ {R}_{c} $平均能控性鲁棒性
    $ {R}_{{\rm{LCC}}} $平均连通鲁棒性
    $ {\boldsymbol{u}} $控制向量
    $ {\cal{V}} $网络节点集合
    $ {\boldsymbol{x}} $状态向量
    $ {\sigma }_{ij} $从节点$ i $到$ j $的最短路径
    $ \Omega $适用解空间
    下载: 导出CSV
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  • 收稿日期:  2020-11-04
  • 网络出版日期:  2021-03-17
  • 刊出日期:  2022-10-14

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