Data-Based Tampered-Data Recovery Strategy With Encoding Against Stealthy Attack for Unknown Discrete-Time Systems

This study addresses a tampered-data recovery problem for linear discrete-time systems with completely unknown system dynamics under stealthy attacks. The basic idea is to identify the stealthy attack, that lies in any of attack-stealthy subspaces, and compensate for it. Different from the existing sparse recovery methods which are applicable to nonstealthy sparse attacks, a novel encoding scheme, where a set of subdecoding matrices is designed specifically for each 1-D attack-stealthy subspace, is developed so that the parameters of the stealthy attack can be identified via a subspace projection technique. A necessary and sufficient condition of determining the targeted subspace by using n parallel attack identification filters is established for this encoding scheme. Especially, a composite encoding matrix characterizes the lower and upper boundaries of the recovery error covariance's trace. A simulation example of a flight vehicle illustrates the efficiency of the proposed approach.