This study investigates the problem of robust fault diagnosis for nonlinear systems subjected to actuator faults and unknown input disturbances. A novel adaptive fast smooth super-twisting observer based on the super-twisting and adaptive dual-layer algorithms is presented, and a robust fault-diagnosis scheme based on an adaptive threshold is proposed to take the estimation error generated by the observer as the residual. In the adaptive fast smooth super-twisting observer, additional fractional powers less than 1 and linear terms are added to improve the smoothness and rapidity of the observer. The finite-time stability of the adaptive fast smooth super-twisting observer is then analyzed based on the Moreno–Lyapunov function algorithm, and rigorous proof confirms that the estimation-error dynamic is robust to unknown input disturbances and can converge to a region of zero in finite time. Finally, simulations of the rigid spacecraft attitude kinematics and dynamics are used to validate the effectiveness of the developed adaptive fast smooth super-twisting observer and the designed robust fault-diagnosis scheme.
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