Kullback–Leibler-Divergence-Based Attacks Against Remote State Estimation in Cyber-Physical Systems

Abstract

This article focuses on investigating the tradeoff problem between the attack stealthiness and the attack performance in cyber-physical systems. The notion of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(\varepsilon,\delta)$</tex-math></inline-formula> -stealthiness is utilized to characterize the stealthiness level, and the corrupted error covariance of the remote estimator is adopted to measure the attack performance. The aim is to design an offline stealthy attack strategy to maximize the attack performance. Different from the existing results, where the relationship between attack performance and system stability is not provided, we prove that the corrupted error covariance has an upper bound for stable systems and can be arbitrarily large for unstable systems. To maximize the attack effect under a given <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(\varepsilon,\delta)$</tex-math></inline-formula> -stealthiness constraint, a nonconvex optimization problem is formulated. By applying convex analysis and monotonic optimization techniques, an upper bound of the attack performance is presented for stable systems. Subsequently, an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(\varepsilon,\delta)$</tex-math></inline-formula> -stealthy attack signal is constructed to achieve the upper bound. Finally, simulations on a stable numerical example and experiments on the permanent magnet synchronous machine monitoring system are performed to demonstrate the theoretical results.