Detection and Performance Compensation for Linear $\epsilon$-Stealthy Attacks in Cyber-Physical Systems

Abstract

In this paper, a precisely designed system framework for linear cyber-physical systems (CPSs) is presented to address the detection and performance compensation problems caused by linear <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\epsilon$</tex-math></inline-formula> -stealthy attacks. In particular, this paper constructs the security modules (data preprocess and data recovery) to assist the detectors (main detector and auxiliary detector) to alert the system anomalies. When no information is leaked, a parameter selection problem is analyzed to help the detector discover the attack. For the cases of model information leakage, we resort to the difference between the main detector and auxiliary detector to reveal the existence of linear <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\epsilon$</tex-math></inline-formula> -stealthy attacks. Under three different attack scenarios, this paper derives the corresponding attack-compensation mechanisms to ensure that the performance losses of systems are bounded. Finally, a three-tank system is provided to verify the effectiveness of the theoretical results.