Optimal Strictly Stealthy Attack Design on Cyber-Physical Systems: A Data-Driven Approach

In this article, an issue of data-driven optimal strictly stealthy attack design for the stochastic linear invariant systems is investigated, with the aim of maximizing the system performance degradation under an energy bounded constraint and bypassing the parity-space-based attack detector. Importantly, the proposed attack policy refrains from the assumption that the system knowledge is known to attackers. A novel strictly stealthy attack sequence (SSAS), coordinating the sensor and actuator signals simultaneously, is proposed with a sufficient and necessary condition for the existence of such an attack presented. Specifically, the SSAS is parameterized as a vector in the null space of a specific matrix which is constructed by a parity matrix and the system Markov parameters. For the purpose of data-driven attack realization, modified subspace identification methods are utilized to achieve an unbiased estimation of the required parameters via the closed-loop data. On this basis, the attack design is formulated as a constrained optimization problem, an explicit solution to which is given to characterize the optimal strictly stealthy attack. Finally, the vulnerability of the cyber-physical systems is analysed from the perspective of the parameter selection for the parity space-based detector. A case study on a three-tank model verifies the efficiency of the proposed approach.