Data-Based Attack Identification Strategy With Complex Field Encoding for Unknown Discrete-Time Systems

This article studies the problem of identifying both stealthy and nonstealthy integrity attacks for unknown linear discrete-time systems. By establishing a necessary and sufficient condition that characterizes stealthy and nonstealthy attacks in a sparse subspace-based form, the considered problem is transformed into the decoupled identification of two subsignals: 1) the subsignal in attack-identifiable space; and 2) the subsignal in attack-unidentifiable space. A novel complex field encoding scheme, through which the two subsignals are projected into different attack-identifiable subspaces, is then proposed so that the two subsignals get identified independently by subspace projection technique. Compared with the previous results that are limited to the identification of either sparse sensor attacks or stealthy ones, the restriction on sparsity is removed and the identification of stealthy attacks is unaffected by nonstealthy ones. Finally, the effectiveness of the proposed approach is illustrated by two simulation examples.