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基于矩阵半张量积的信息物理融合系统状态不透明性分析与控制

张志鹏 许倩 夏承遗

张志鹏, 许倩, 夏承遗. 基于矩阵半张量积的信息物理融合系统状态不透明性分析与控制[J]. 电子与信息学报, 2021, 43(12): 3434-3441. doi: 10.11999/JEIT210492
引用本文: 张志鹏, 许倩, 夏承遗. 基于矩阵半张量积的信息物理融合系统状态不透明性分析与控制[J]. 电子与信息学报, 2021, 43(12): 3434-3441. doi: 10.11999/JEIT210492
Zhipeng ZHANG, Qian XU, Chengyi XIA. Semi-tensor Product of Matrices-based Approach to the Opacity Analysis of Cyber Physical Systems[J]. Journal of Electronics & Information Technology, 2021, 43(12): 3434-3441. doi: 10.11999/JEIT210492
Citation: Zhipeng ZHANG, Qian XU, Chengyi XIA. Semi-tensor Product of Matrices-based Approach to the Opacity Analysis of Cyber Physical Systems[J]. Journal of Electronics & Information Technology, 2021, 43(12): 3434-3441. doi: 10.11999/JEIT210492

基于矩阵半张量积的信息物理融合系统状态不透明性分析与控制

doi: 10.11999/JEIT210492
基金项目: 国家自然科学基金(62173247)
详细信息
    作者简介:

    张志鹏:男,1990年生,讲师,研究方向为信息物理系统的隐私分析与安全控制、博弈控制

    许倩:女,1996年生,硕士生,研究方向为信息物理系统的隐私分析

    夏承遗:男,1976年生,教授,研究方向为复杂网络传播、演化博弈理论、大数据分析和信息安全

    通讯作者:

    夏承遗 xialooking@163.com

  • 中图分类号: TP1

Semi-tensor Product of Matrices-based Approach to the Opacity Analysis of Cyber Physical Systems

Funds: The National Natural Science Foundation of China (62173247)
  • 摘要: 状态不透明性作为一种重要的机密属性,能够表征入侵者窃取系统隐私信息的能力。针对带有不可观测事件的信息物理融合系统(CPSs),该文提出一种基于矩阵半张量积(STP)的代数状态空间方法,并且分析与验证CPSs的状态不透明性。首先利用矩阵STP理论对CPSs的状态演化进行建模,得到系统的动态代数表达式,然后利用STP运算的特性,给出验证系统当前状态不透明性的充分必要代数条件。最后,通过数值仿真算例验证了方法的有效性。该文提出的基于矩阵STP方法为CPSs相关隐私分析与安全控制研究提供了一个新的思路和框架。
  • 图  1  系统$A = \left( {X,E,{E_o},\sigma ,{x_0}} \right)$

    图  2  验证算法的流程图

    表  1  常用符号

    概念定义
    ${\mathbb{N}^ + }$正整数的集合
    ${\mathbb{R}^n}$维数为$n$的所有实向量的集合
    $\left| X \right| = n$集合$X$的基数
    ${\mathbb{R}^{n \times m}}$维数为$n \times m$的实矩阵集
    ${\mathbb{B}^{n \times m}}$维数为$n \times m$的布尔矩阵集
    ${\boldsymbol{R}}\left( {i,j} \right)$矩阵${\boldsymbol{R}}$的第$i$行第$j$列元素
    ${\text{Co} }{ {\text{l} }_i}\left( {\boldsymbol{R}} \right)$, ${{\rm{Row}}_j}\left( {\boldsymbol{R} } \right)$分别为矩阵${\boldsymbol{R}}$的第$i$列,第$j$行
    ${\rm{Col}}\left( {\boldsymbol{R} } \right)$, ${\rm{Row}}\left( {\boldsymbol{R} } \right)$矩阵${\boldsymbol{R}}$的所有列和所有行的集合
    ${{\boldsymbol{I}}_n}$维数为$n$的单位矩阵
    $\delta _n^i$单位矩阵${{\boldsymbol{I}}_n}$的第$i$列
    ${\varDelta _n}$$\left\{ {\delta _n^1,\delta _n^2, \cdots ,\delta _n^n} \right\}$
    ${2^X}$集合$X$的幂集合
    $\displaystyle\sum\nolimits_\mathbb{B}^{i \in R} { {{\boldsymbol{M}}_i} }$所有$i \in {\boldsymbol{R}}$矩阵${{\boldsymbol{M}}_i}$的布尔和
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-06-01
  • 修回日期:  2021-10-29
  • 网络出版日期:  2021-11-14
  • 刊出日期:  2021-12-10

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