Securing Cyber-Physical Systems Under Periodic Detection: Optimal Stealthy Linear Attack and Countermeasure

Security issues are of significant importance for cyber-physical systems (CPS), where the attack design is a major concern. Most related studies on attack design implicitly assume that the control and detection periods are the same. However, the two periods could be different in practical systems with remote detection such as supervisory control and data acquisition (SCADA) systems, which could lead to new vulnerabilities for attackers. In this paper, we consider the design of innovation-based stealthy linear attack strategies for CPS when the control period and detection period are inconsistent. Specifically, we propose an attack framework that consists of attack strategies for detection and non-detection instants under the period discrepancy. On this basis, we design the optimal stealthy innovation-based linear attack strategies for state estimation and Linear Quadratic Gaussian (LQG) control to maximize the estimation error and control cost, respectively. We then prove that the estimation error and controller cost caused by the attacker are bounded. We further propose a countermeasure combining a secure module based on the pseudo-random number (PRN) technique with the multivariate exponentially weighted moving average (MEWMA) detector to help detect this type of attack. Simulations are given to demonstrate the effectiveness of the proposed attack strategies and the countermeasure.