Optimal Stealthy Joint Attacks against Distributed State Estimation in Cyber-Physical Systems

This article studies the design of the optimal stealthy joint attacks against distributed state estimation in cyber-physical systems to steer the state estimates in all the sensors as close as possible to a common target within finite time. To ensure stealthiness, both the Kullback-Leibler divergence between the innovations and the Kullback-Leibler divergence between the consensus errors with and without attacks at each instant should not exceed given thresholds, respectively. In the case that all the thresholds equal to zero, the optimal attack is given in the form of an analytical expression. In the cases that some thresholds are larger than zero, an optimization problem is solved for each case at each instant, and the corresponding attack sequence obtained is proved to be globally optimal. Finally, a numerical example is adopted to verify the effectiveness of the proposed optimal attack strategies.