Design of Stealthy Attacks Against Interval Estimation for Cyber-Physical Systems

This paper focuses on the design of stealthy attacks for cyber-physical systems (CPSs) with unknown but bounded process disturbances and measurement noises. To effectively address the impact of unknown disturbances on state estimation, interval estimation techniques are utilized. In this work, the optimal attack objective that forces the system state out of the interval estimation range is obtained, as the adversaries do not need to require information about the estimator coordinate transformation. Then, considering detection based on decoupled parity equations, the final sequence of attacks is derived by iteratively solving the linear programming problem, with the constraints that the attacks remain stealthy at the current time and do not affect the residuals afterward. Furthermore, the condition for the existence of attacks satisfying the stealthy constraints is presented. Finally, the effectiveness of the proposed attack strategy is verified by a numerical example.