Event-Driven Output-Watermarking for Replay Attack Detection of Cyber-Physical Systems

This paper introduces a novel event-driven output watermarking scheme for replay attack detection of cyber-physical systems. Conventional input-watermarking techniques continuously embed watermarks into control inputs, inevitably degrading control performance. In contrast, the proposed method departs from them by employing on-demand, event-triggered embedding directly into system outputs. This strategic shift eliminates the persistent performance penalty associated with input-based methods while ensuring reliable detection by selectively utilizing high-amplitude watermark signals. Furthermore, unlike existing heuristic approaches, a systematic parameter design framework is further developed to analytically reveal the impact of key parameters such as embedding frequency and signal covariance on detection reliability. By formulating the covariance design as a convex optimization problem, the framework enables automated synthesis of near-optimal watermarks under practical constraints. Theoretical and simulation results confirm that the proposed output-watermarking strategy not only bypasses the forward-path filtering effects inherent in input-based methods but also yields a more significant deviation in the residual distribution, thereby improving detection performance without increasing the false-alarm rate. The scheme provides a scalable, resource-efficient, and control-preserving solution for securing CPSs against stealthy replay attacks.