Hua Yi, Wan Fangyi, Gan Hongping, Zhang Youmin, Qing Xinlin
IEEE Trans Cybern. 2023 Sep;53(9):5840-5853. doi: 10.1109/TCYB.2022.3197591. Epub 2023 Aug 17.
Under false data-injection (FDI) attacks, the data of some agents are tampered with by the FDI attackers, which causes that the distributed algorithm cannot estimate the ideal unknown parameter. Due to the concealment of the malicious data tampered with by the FDI attacks, many detection algorithms against FDI attacks often have poor detection results or low detection efficiencies. To solve these problems, a conveniently distributed diffusion least-mean-square (DLMS) algorithm with cross-verification (CV) is proposed against FDI attacks. The proposed DLMS with CV (DLMS-CV) algorithm is comprised of two subsystems: one subsystem provides a detection test of agents based on the CV mechanism, while the other provides a secure distribution estimation. In the CV mechanism, a smoothness strategy is introduced, which can improve the detection performance. The convergence performance of the proposed algorithm is analyzed, and then the design method of the adaptive threshold is also formulated. In particular, the probabilities of missing alarm and false alarm are examined, and they decay exponentially to zero under sufficiently small step size. Finally, simulation experiments are provided to illustrate the effectiveness and simplicity of the proposed DLMS-CV algorithm in comparison to other algorithms against FDI attacks.
在虚假数据注入（FDI）攻击下，一些智能体的数据被FDI攻击者篡改，这导致分布式算法无法估计理想的未知参数。由于FDI攻击篡改的恶意数据具有隐蔽性，许多针对FDI攻击的检测算法往往检测结果不佳或检测效率较低。为了解决这些问题，提出了一种具有交叉验证（CV）功能的便捷分布式扩散最小均方（DLMS）算法来对抗FDI攻击。所提出的带CV的DLMS（DLMS-CV）算法由两个子系统组成：一个子系统基于CV机制对智能体进行检测测试，而另一个子系统提供安全的分布式估计。在CV机制中，引入了一种平滑策略，可提高检测性能。分析了所提算法的收敛性能，进而制定了自适应阈值的设计方法。特别地，研究了漏警和误警的概率，在足够小的步长下它们会指数衰减至零。最后，通过仿真实验说明了所提DLMS-CV算法相对于其他对抗FDI攻击算法的有效性和简易性。
