Malicious adversaries against secure state estimation: Sparse sensor attack design

Abstract

This paper investigates the sparse sensor attack design problem for a class of cyber–physical systems equipped with state estimators, attack detectors and secure state estimators. Two regimes of attacks are considered: undetectable attacks and unidentifiable attacks. First, through constructing a novel attack model where adversaries make estimators track the state of a target system instead of tracking the original system state, necessary and sufficient conditions for the existence of undetectable attacks are provided and an undetectable attack design strategy is proposed such that the adversary can worsen the estimation performance without being detected. Second, based on the analysis for undetectable attacks, a necessary and sufficient condition for the existence of unidentifiable attacks is also provided. For the adversary who cannot compromise enough channels for designing undetectable attacks, an unidentifiable attack design strategy is proposed such that secure state estimators cannot determine which channels are attacked. Different from the existing methods mainly considering undetectable attacks, investigating unidentifiable attacks shows that the adversary has the ability to affect the state estimate greatly even if secure state estimators are adopted. Finally, a numerical simulation is provided to illustrate the correctness and effectiveness of the proposed conditions and methods.