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 counter...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 stationary 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 steadystate 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 operation are derived.Finally,a novel zonotopically bounded watermark 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 illustrated in simulation using a quadruple-tank process.展开更多
基金in part supported by the Margarita Salas grant from the Spanish Ministry of Universities funded by the European Union NexGenerationEUin part co-funded by the Spanish State Research Agency(AEI)and the European Regional Development Fund(ERFD)through the project SaCoAV(ref.MINECO PID2020-114244RBI00)。
文摘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 stationary 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 steadystate 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 operation are derived.Finally,a novel zonotopically bounded watermark 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 illustrated in simulation using a quadruple-tank process.
