Optimal stealthy false data injection attacks in cyber-physical systems

In this paper, the problem of false data injection attacks for cyber-physical systems is investigated. The Kullback-Leibler divergence is utilized to measure the stealthiness of the attacks. Different from the existing attack policies which are required to be zero-mean Gaussian distributed, a more general linear attack strategy based on Gaussian distribution with an arbitrary mean is proposed. Under the framework of the attacks, the degradation of system performance is analyzed by utilizing the statistical characteristics of the measurement innovation, and the optimal attack strategy is obtained by employing the Lagrange multiplier method to solve a constrained quadratic optimization problem. It is proved that the developed attack scheme can achieve the largest remote estimation error and guarantee the attack stealthiness simultaneously. Finally, simulation examples are provided to demonstrate the theoretical results. (C) 2019 Elsevier Inc. All rights reserved.