## 1 Introduction
In [14], a neural network observer is developed to reconstruct the lumped disturbance, while an active event-based dual-channel control scheme is created to solve accurate attitude stabilization under limited communication. Based on the nonsingular terminal sliding-mode theory, an active reconfiguration FTC method is proposed in [15], where a Chebyshev neural network is used to update and compensate for the lumped disturbance. For robust attitude fault-tolerant stabilization, a neural network-based third-order SMC method is proposed in [16], where a neural network is suggested to reconstruct the lumped uncertainty. It is worth pointing out that integral-based adaptive learning algorithms [9; 10] and various neural networks with multi-level nodes [13; 14; 15; 16] require massive computational power. Recently, learning algorithm-based fault reconstruction and active attitude FTC for spacecraft systems have attracted considerable attention, and fruitful results have been published. At present, various types of learning algorithms have been developed to provide system fault (or disturbance) information, such that they could be applied to fault reconstruction and accurate tolerant control for spacecraft systems. An iterative learning observer (ILO) is firstly designed to reconstruct thruster faults of spacecraft systems in [17], providing a contrasting analysis of computation burden between the ILO and the integrator-based adaptive observer. In [18], a repetitive learning observer (RLO) is developed for actuator fault detection, isolation, and reconstruction for satellite ACS. In [19], an ILO-based attitude sliding-mode fault-tolerant stabilization control approach is proposed for the satellite subjects to external disturbance and actuator constraints, and an ILO is designed to reconstruct loss of actuator effectiveness faults. In [20], a linear LO is designed for actuator fault reconstruction for a microsatellite ACS. However, a linear satellite ACS model inevitably results in modeling errors. Based on the iterative learning algorithm, an online-learning spacecraft attitude stabilization control approach is investigated in [21]. ILO-based adaptive learning control for spacecraft attitude stabilization is investigated in [22], where a barrier function-based ILO is proposed to estimate the lumped disturbance, including actuator faults, parameter uncertainty, and external disturbance. At present, two types of learning algorithms, including an iterative learning algorithm and a repetitive learning algorithm, have been separately developed for fault reconstruction and tolerant control for spacecraft systems. Considering the advantages of the two learning algorithms, a mixed learning observer (MLO)-based actuator fault reconstruction method for space craft system has been devised. In [23], an MLO is proposed by combining the iterative learning algorithm and the repetitive learning algorithm. Based on [23], an MLO-based active prescribed performance consensus control for multiagent systems is developed. An MLO-based closed-loop attitude proportional-derivative stabilization control approach is proposed in [24], where an MLO is adopted to compensate for the lumped disturbance. However, parameter selection and computation are not handled well. Therefore, motivated by practical considerations, mixed learning algorithm-based active attitude FTC for the spacecraft is a considerably interesting research topic. In [25], an adaptive LO is designed to reconstruct actuator faults, while an adaptive backstepping fault-tolerant controller is designed to guarantee accurate attitude tracking. In [26], an iterative learning observer with the sliding mode term is explored to robustly reconstruct actuator faults, while an iterative learning sliding mode controller is used to actively stabilize the spacecraft attitude. However, the robustness inevitably decreases fault convergence speed.