Co-Design of Watermarking and Controller for Reducing Detection Delay of Replay Attacks

This paper investigates the problem of reducing the detection delay of the replay attacks by co-designing the watermarking signal and the controller parameters. Based on the dynamic encryption-decryption scheme, we propose a cumulative sum test, which utilizes the sensor measurements and watermarking signals to detect the replay attacks, and derive the relationship between the detection delay and the watermarking signal covariance. Then, we analyze the control performance loss caused by the watermarking signal added to the sensor measurements to expose the replay attacks. Furthermore, to reduce the detection delay, an optimization problem is formulated to design the optimal covariance of the watermarking signal with a tolerable control performance loss. Finally, we reformulate another optimization problem of co-designing the watermarking signal and the controller parameters to simultaneously reduce the detection delay and the control performance loss. A numerical example is provided to verify the effectiveness of theoretical results.