Secure state and fault interval estimation for wastewater treatment systems under stealthy attacks via T-N-L observer

In this paper, the secure state and fault estimation methods are studied for wastewater treatment systems subject to stealthy cyber attacks, actuator faults, and system uncertainties. First, a T–S fuzzy model is developed to characterize the complex nonlinear dynamics of the wastewater treatment processes (WWTPs), and a corresponding discrete-time state-space model is constructed. Second, a T-N-L structured observer is designed to achieve simultaneous estimation of system states and actuator faults. To handle the adverse effects of stealthy attacks and bounded disturbances, an ellipsoidal set analysis method is used to recursively compute interval bounds for the states and faults. Third, the stability and L ∞ -gain performance of the proposed observer are rigorously analyzed, and sufficient conditions are derived in terms of linear matrix inequalities (LMIs). Furthermore, the upper and lower bounds of stealthy attack signals are derived by using reachable set analysis, ensuring the integrity of interval estimation. Simulation results based on a benchmark wastewater treatment model demonstrate the effectiveness of the proposed method in terms of estimation accuracy, fault detection capability, and robustness against stealthy attacks. Overall, this study provides a reliable foundation for the secure and resilient operation of WWTPs.