Measurement-Based Optimal Stealthy Attacks on Remote State Estimation

This paper focuses on designing measurement-based optimal stealthy attacks for linear cyber-physical systems (CPSs), where attackers aim to deteriorate the performance of remote state estimation and keep
$\epsilon $
-stealthy to Kullback-Leibler divergence detector. Instead of constructing a linear attack directly, we consider a more general attack model with an arbitrary distribution to reveal the correlations between attacks and the stealth level
$\epsilon $
. By solving a convex optimization problem, the mean and variance of optimal attacks on common unprotected systems are obtained. Not limited to zero mean Gaussian attacks, the derived optimal attacks can also obey non-zero mean Gaussian distribution and degenerate to the former in some special cases. For protected systems equipped with encryption procedures, a general criterion for the selection of attacked channels is given. Finally, an unmanned aerial vehicle (UAV) example is provided to verify the effectiveness of the theoretical results.