## 1 Introduction  
In order to achieve various advanced space missions, such as Earth observation, remote communication, navigation, and positioning, considerable research work has been performed on spacecraft attitude control, including attitude stabilization, attitude tracking, etc. [1; 2]. For the above two attitude maneuvers, certain prescribed attitudes or attitude velocities within certain ranges are required for a spacecraft during its mission life. The diversity of space missions and the growing requirements for high performance unavoidably result in increasingly sophisticated attitude control systems (ACSs). On the other hand, the extremely harsh outer space environment and the aging of actuators raise the probability of malfunctions in spacecraft actuators to a certain extent, resulting in significant performance degradation or task paralysis [3]. Therefore, it is extremely necessary for the spacecraft ACS to possess the fault-tolerant capability that maintains the desired attitude performance properties. Plenty of research progress on spacecraft attitude control methods with fault tolerance has been reported, with recent progress published in [1; 4; 5] and the references therein. It is widely acknowledged that fault-tolerant control (FTC) can be divided into two categories, namely, passive FTC and active FTC [6; 7]. In the former FTC design, online fault information is not necessary, and it has the ability to deal with presumed faults, not all faults. However, this design has limited fault-tolerant capabilities, and the desired control performance cannot be guaranteed for unanticipated fault scenarios. Alternatively, an active FTC reacts to system faults actively by resorting to a reconfigurable controller [7]. The active FTC scheme can be further divided according to whether a fault detection and isolation (FDI) unit exists. The active FTC scheme involving an FDI unit requires fault diagnostic information on occurrence time and location. However, time-delay issues inevitably affect the overall system control performance under this FTC scheme. In contrast, the active FTC without FDI can compensate for system fault effects, and such FTC approaches mainly contain adaptive mechanism-based FTC [8] and fault reconstruction-based FTC. At present, various fault-reconstruction methods have been developed for spacecraft ACSs, e.g., adaptive observer [9; 10], sliding mode observer [11; 12], and neural network observer [13; 14], just to name a few. Furthermore, based on different fault-reconstruction observers, recent progress on active attitude FTC strategies have been developed to actively compensate for actuator faults by utilizing reconfigurable fault-tolerant controllers; see, for example, [9; 10; 11; 12; 13; 14; 15; 16]. In [9], an adaptive indirect estimator is proposed to reconstruct actuator faults, while a fault-tolerant steering logic design is investigated for spacecraft with a single-gimbal control moment gyro. In [10], an adaptive finite-time observer is designed to reconstruct the lumped faults, while an adaptive integral sliding mode control (SMC) method is proposed to achieve spacecraft active attitude FTC. In [11], an adaptive sliding mode observer is proposed to reconstruct actuator loss of effectiveness, and an integrated fault-reconstruction/FTC scheme is developed based on a fractional-order nonsingular terminal sliding mode method and backstepping technology. A robust nonlinear disturbance observer (RNDO)-based adaptive non-singular fast terminal SMC method is proposed in [12], where an RNDO with the sliding mode is proposed to reconstruct the lumped disturbance, including actuator faults, inertia uncertainties, and external disturbances. However, the chatting phenomenon resulting from the sliding modes [11; 12] is inevitable. In [13], a neural network observer is used to reconstruct unknown faults while the sliding mode controller is designed to guarantee the attitude convergence in finite time.