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摘要: 研究了信息物理系统中假数据注入(False data injection, FDI)攻击信号的检测问题. 在分布式融合框架下, 首先将FDI攻击信号建模为信息物理系统模型中的未知输入, 从而使得攻击信号的检测问题转化为对FDI攻击信号的实时估计问题. 其次, 在每个传感器端设计基于自适应卡尔曼滤波的FDI攻击信号的局部估计器; 在融合中心端引入补偿因子, 设计分布式信息融合准则以导出攻击信号的融合估计器. 特别地, 当FDI攻击信号是时变情况时, 融合过程中补偿因子的引入可以大大提高对攻击信号的估计精度. 最后, 通过两个仿真算例验证所提算法的有效性.
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关键词:
- 自适应Kalman滤波 /
- 假数据注入攻击 /
- 攻击信号估计 /
- 信息融合
Abstract: This paper is concerned with the estimation problem of false data injection (FDI) attacks in cyber-physical systems, where the false data is injected into the actuator. Under the distributed fusion framework, the attack signal is modeled as an unknown parameter in the addressed system models, and each local estimate of the attack signal at the sensor is obtained based on adaptive Kalman filtering method. Subsequently, by introducing the compensation factor, an optimal weighing fusion criterion is designed to improve estimation precision of attack signals. Particularly, when the FDI attack signal is time-varying, the introduction of compensation factor during fusing process can indeed improve the estimation precision largely. Finally, two illustrative examples are used to show the effectiveness of the proposed methods. -
图 1 算例1: 情况1中攻击信号和融合估计的轨迹
Fig. 1 Example 1: The trajectories of attack signal and its fusion estimation under Case 1
图 2 算例1: 情况1中攻击信号的局部估计器与融合估计器之间的性能比较
Fig. 2 Example 1: The performance comparison between local estimators and fusion estimators under Case 1
图 3 算例1: 情况2中攻击信号和融合估计轨迹
Fig. 3 Example 1: The trajectories of attack signal and its fusion estimation under Case 2
图 4 算例1: 情况2中攻击信号的局部估计器与融合估计器之间的性能比较
Fig. 4 Example 1: The performance comparison between local estimators and fusion estimators under Case 2
图 5 算例1: 情况2中不同补偿因子下攻击信号融合估计性能的比较
Fig. 5 Example 1: The comparison of fusion estimation performance of attack signal under different compensation factors under Case 2
图 6 算例1: 情况2中不同补偿因子下攻击信号融合估计的轨迹
Fig. 6 Example 1: The trajectories of fusion estimation of attack signal under different compensation factors under Case 2
图 7 算例2: 不同补偿因子下攻击信号融合估计的轨迹
Fig. 7 Example 2: The trajectories of fusion estimation of attack signal under different compensation factors
图 8 算例2: 不同补偿因子下攻击信号融合估计性能的比较
Fig. 8 Example 2: The comparison of fusion estimation performance of attack signal under different compensation factors
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