A new watermarking approach for replay attack detection in LQG systems

The problem of detecting replay attack to the linear stochastic system with Kalman filer state estimator and LQG controller is addressed. Under replay attack to output measurements of the system, a dynamic watermarking method is proposed which is dependent on the dynamics of the system as well. While preserving the stability of the main system, the conditions on the parameters of the watermarking dynamics is obtained so that the attack can be revealed by destabilization of a residual trajectory which is the difference between the estimated and measured output of the system. Using this method, defender can adjust the detection rate of the system by changing the design parameters. Nevertheless, since the exogenous watermarking signal affects the performance of the controlled system, we propose an optimization problem to determine such a watermarking signal with the minimum loss effect. In the simulation results, the proposed dynamic watermarking approach is compared with the additive white noise watermarking method and the results confirm the superiority of the new scheme.