Optimal periodic watermarking schedule for replay attack detection in cyber–physical systems

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We consider periodic watermarking scheduling for detecting discontinuous replay attacks in Cyber–Physical Systems (CPSs). The existing methods of imposing continuous watermarks on the nominal control inputs may result in the waste of control cost when system detectors are not sensitive to the added watermarks, since the attacker may be absent for a considerably long time. For example, in the famous Stuxnet event, the attacker only launches the attack for a short period each month in order to avoid being detected. In this paper, we firstly formulate a one-time attack duration model for such discontinuous replay attacks. Then, by exploiting the attack model, we propose a periodic watermarking strategy which aims to reduce the control cost. Furthermore, we obtain an optimal periodic watermarking strategy for the approximate detection performance. Extensive simulations over a quadruple water tank system are provided to demonstrate the effectiveness of the proposed strategy.