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A fault detection and isolation (FDI) algorithm is proposed for the stuck fault detection of an aircraft with multiple control surfaces. The proposed FDI approach is composed of an adaptive observer and a bias estimation algorithm. The adaptive observer is designed for the stuck fault detection of the control surfaces, and the bias estimation algorithm is used to estimate the stuck position of the corresponding control surface. The bias estimation algorithm is designed using an unscented Kalman filter. Non-linear back-stepping control is applied. Also, to achieve the fault-tolerant property without redesigning the controller, control allocation technique is used. A non-linear aircraft model with the multiple control surfaces is considered. Numerical simulations are performed to demonstrate the performance of the proposed FDI algorithm.