Optimal Intermittent Deception Attacks With Energy Constraints for Cyber–Physical Systems

This article investigates the intermittent deception attacks against the remote state estimation for cyber–physical systems, where two kinds of energy constraints are considered to, respectively, restrict the dwell times and total times of deception attacks. For the strictly stealthy attacks, it is proved that flipping the sign of the nominal innovation is always optimal under any given schedule in both holistic and one-step optimization designs, which significantly simplifies the collaborative design of attack schedules and matrices. For the
$\delta$
-stealthy attacks, the analytical expression of the optimal attack matrices is derived by adopting the data isolation technique without the assumption required in the existing results that the output matrix is of full row rank. Since the constraint conditions for the dwell times which are employed in the related works are nonlinear such that the transformed 0-1 programming problem is difficult to solve, an equivalent condition is proposed in a linear form by taking advantage of the sliding window technique, based on which the optimal attack schedule is obtained. Finally, simulation examples are illustrated to verify the effectiveness of the proposed attack policies.