Optimal Stealthy Attacks With Energy Constraint Against Remote State Estimation

This article investigates the problem of energy-constrained stealthy attack strategy against remote state estimation for cyber-physical systems. Taking into account the energy constraint, the malicious attacker is required to schedule the off-line generated signals to modify the transmitted data with limited times over a finite-time horizon under the stealthiness condition, which makes the design of attack strategy more complex. Different from the attack schedules which are studied on the basis of prescribed attack signals in the existing results, the attack strategy is presented under the framework of collaborative design to deteriorate the estimation performance to the largest extent, which yet leads to the coupling between the attack schedules and attack signals. To overcome the difficulty without sacrificing the optimality, the attack design problem is solved in two steps. First, analyze the problem with the given attack schedule to derive the optimal attack signals. Then, the optimal schedule is obtained by efficiently solving the nonlinear 0–1 programming problem based on the algorithm of reducing the search space which is designed to eliminate a part of the nonoptimal solutions. To demonstrate the theoretical results, a simulation example is provided.