Worst-Case Stealthy Innovation-Based Linear Attacks on Remote State Estimation Under Kullback-Leibler Divergence

With the wide application of cyber-physical systems, stealthy attacks on remote state estimation have attracted increasing research attention. Recently, various stealthy innovation-based linear attack models were proposed, in which the relaxed stealthiness constraint was based on the Kullback-Leibler divergence. This article studies existing innovation-based linear attack strategies with relaxed stealthiness and concludes that all of them provided merely suboptimal solutions. The main reason is some oversight in solving the involved optimization problems: some covariance constraints were not perfectly handled. This article provides the corresponding optimal solutions for those stealthy attacks. Both one-step and holistic optimizations of stealthy attacks are studied, and the worst-case attacks with and without zero-mean constraints are derived analytically, without the necessity to numerically solve semidefinite programming problems.