Optimal Stealthy Linear Man-in-the-Middle Attacks With Resource Constraints on Remote State Estimation

Abstract

This article studies the impact of constrained optimal stealthy attacks on the state estimator, where man-in-the-middle attacks with a linear form can compromise innovations transmitted through a wireless network. First, a novel resource-constrained attack model is proposed, in which there are only a finite number of attack instants within a fixed interval. Second, the evolution of the estimation error covariance under attacks is obtained, and the covariance at the ultimate instant of the attack interval is regarded as the attacker’s cost function. Moreover, a relaxed condition of the strict stealthiness, named Kullback–Leibler divergence, is employed to describe the attacker’s the stealthiness metric. Third, the one-time and holistic optimization problems of stealthy attacks are solved by exploiting the Lagrange multiplier method. Then the constrained optimal attack strategies are obtained to produce the largest ultimate estimation error covariance. Finally, two simulation cases are provided to confirm the correctness of the designed attack strategies.