This paper suggests the use of zonotopes for the design of watermark signals. The proposed approach exploits the recent analogy found between stochastic and zonotopic-based estimators to propose a deterministic counterpart to current approaches that study the replay attack in the context of station-ary Gaussian processes. In this regard, the zonotopic analogous case where the control loop is closed based on the estimates of a zonotopic Kalman filter (ZKF) is analyzed. This formulation allows to propose a new performance metric that is related to the Frobenius norm of the prediction zonotope. Hence, the steady-state operation of the system can be related with the size of the minimal Robust Positive Invariant set of the estimation error. Furthermore, analogous expressions concerning the impact that a zonotopic/Gaussian watermark signal has on the system opera-tion are derived. Finally, a novel zonotopically bounded water-mark signal that ensures the attack detection by causing the residual vector to exit the healthy residual set during the replay phase of the attack is introduced. The proposed approach is illus-trated in simulation using a quadruple-tank process.

Carlos Trapiello;Vicen? Puig

Supervision,Safety and Automatic Control Research Center(CS2AC)of the Universitat Politécnica de Catalunya(UPC),Rambla Sant Nebridi,22,08222 Terrassa,Spain;UMR 5218-IMS Laboratory,France;Supervision,Safety and Automatic Control Research Center(CS2AC)of the Universitat Politécnica de Catalunya(UPC),Rambla Sant Nebridi,22,08222 Terrassa;Institut de Robòtica i Informàtica Industrial(CSIC-UPC),Carrer Llorens Artigas,4-6,08028 Barcelona,Spain

自动化学报（英文版）

[1]Carlos Trapiello;Vicen? Puig-.A Zonotopic-Based Watermarking Design to Detect Replay Attacks)[J].自动化学报（英文版）,2022(11):1924-1938

Zonotopic,zonotopes,watermark,zonotopic,ZKF,zonotope,zonotopically

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