非减损动态系统抗稀疏完整性攻击的高效安全状态估计
Efficient Secure State Estimation against Sparse Integrity Attack for System with Non-derogatory Dynamics
摘要：
我们考虑的问题估计的时不变的线性高斯系统的完整性攻击的存在下的状态。攻击者可以危害$m$传感器中的$p$，并且任意地操纵测量，所述$m$传感器的集合随时间是固定的并且对于系统操作员是未知的。在假设系统矩阵$A$的所有不稳定特征值的几何重数为1（$A$的不稳定部分是非减损的）的条件下，提出了一种只要系统是$2p$ -稀疏可检测的就能抵抗完整性攻击的安全动态估计方案，并证明了这是安全动态估计的基本极限.在没有攻击的情况下，所提出的估计符合卡尔曼估计与一定的概率，可以调整到性能与无攻击之间的权衡。此外，设计阶段的可探测性条件检查和在线运行阶段的估计计算都是计算高效的。一个数值例子来证实的结果，并说明所提出的估计的性能。
英文摘要：
We consider the problem of estimating the state of a time-invariant linear Gaussian system in the presence of integrity attacks. The attacker can compromise $p$ out of $m$ sensors, the set of which is fixed over time and unknown to the system operator, and manipulate the measurements arbitrarily. Under the assumption that all the unstable eigenvalues of system matrix $A$ have geometric multiplicity 1 (unstable part of $A$ is non-derogatory), we propose a secure estimation scheme that is resilient to integrity attack as long as the system is $2p$-sparse detectable, which is proved to be the fundamental limit of secure dynamic estimation. In the absence of attack, the proposed estimation coincides with Kalman estimation with a certain probability that can be adjusted to trade-off between performance with and without attack. Furthermore, the detectability condition checking in the designing phase and the estimation computing in the online operating phase are both computationally efficient. A numerical example is provided to corroborate the results and illustrate the performance of the proposed estimator.
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