Set-Theoretic Control for Active Detection of Replay Attacks with Applications to Smart Grid

In this paper, we propose a novel physical watermarking technique for the active detection of replay attacks in cyber-physical systems. The proposed strategy exploits the set-theoretic model predictive control paradigm to design control input that, whenever needed, can be safely and continuously applied to the system for an apriori known number of steps. Such a control scheme enables the design of a physical watermarked control signal that is obtained by properly randomly dropping the last computed command input. As an example application, we apply the proposed control scheme to the IEEE new England 39-bus system. We prove that, in the attack-free case, the generators' transient stability is achieved for all admissible watermarking signals and that the closed-loop system enjoys uniformly ultimately bounded stability. Our simulation results confirm that the proposed solution is effective in detecting replay attacks and is also capable of mitigating the control performance loss drawback typical of watermarking solutions.