Watermarking-based Discrete LQG Systems for Detecting Replay Attacks

The problem of detecting replay attacks on discrete-time stochastic systems using Kalman filter state estimators and LQG controllers is studied. A dynamic watermarking method based on the dynamic characteristics of the system is proposed to deal with the replay attack on the output measurement values. The stability of the main system is maintained, and the condition of the dynamic parameters of the watermark is given, so that the attack can be revealed by the instability of the difference between the estimated output and the measured output, i. e. the residual trajectory. This method adjusts the detection rate of the system by changing the design parameters of the system. However, because the designed watermark signal will affect the performance of the controlled system, an optimal control method is adopted to minimize the loss caused by the watermark signal. Simulation results show that the proposed dynamic watermarking method has better performance than the additive white noise watermarking method.