Optimal Innovation-Based Stealthy Attacks in Networked LQG Systems With Attack Cost

In this article, the optimal innovation-based attack strategy is investigated for the networked linear quadratic Gaussian (LQG) systems. To bypass the detector, the attacks are required to follow strict stealthiness or
$\epsilon $
-stealthiness described by the Kullback–Leibler divergence. The attackers aim to increase the quadratic control cost and decrease the attack cost, which is formulated as a nonconvex optimization problem. Then, based on the cyclic property of the matrix trace, the nonconvex objective function is transformed into a linear function related to attack matrices and covariance matrices of the tampered innovations. The optimal strictly stealthy attack is obtained by utilizing the matrix decomposition technique. Furthermore, the optimal
$\epsilon $
-stealthy attack is derived to achieve a higher-attack effect by an integrated convex optimization, which distinguishes from the existing suboptimal attacks developed by a two-stage optimization. Simulation results are provided to show the effectiveness of the designed attacks.