Optimal Stealthy Innovation-Based Attacks With Historical Data in Cyber-Physical Systems

The problem of stealthy innovation-based attacks in cyber-physical systems is studied in this paper. Different from the existing results which only utilize the current data, a more general attack strategy is designed by combining the historical and the current innovations to deteriorate the estimation performance and keep stealthy to the detector simultaneously. Under the framework of the attacks, the remote state estimation error is analyzed, and the optimal attack policy is derived by solving a convex optimization problem to achieve the maximal estimation error. Moreover, it is proved that the optimal attack strategy is piecewise constant, such that the attack is designed with low calculation cost. Finally, simulation examples are provided to demonstrate the theoretical results.