## 1 Introduction
For example, predictive control [1], backstepping control [16], adaptive control [3], fuzzy control [17], control [18] based on neural network, etc. In [16], a second-order system of actuators is established to describe actuator failure (LOE) and stuck faults, which provides a basis for subsequent fault diagnosis and identification (FDI) design.Then, fault-tolerant control strategies resting on FDI and backstepping control are developed to achieve the control objective; however, such accurate actuator models are difficult to establish. In [17], the Takagi-Sugeno (T-S) fuzzy model is applied to describe the attitude dynamics of a near-space vehicle in the case of actuator failure. Then, the adaptive fault-tolerant tracking control is implemented by using the estimated actuator faults, but there is no suitable fuzzy rule to describe the faulty aircraft. In addition, an adaptive output feedback fault-tolerant controller is designed in [19] to handle parameter uncertainties, actuator failures and external disturbances in HSV attitude systems. Therefore, such a large number of adaptive learning parameters can create a heavy online computational load. In addition, based on the strong robustness of sliding mode control and its modified control strategies are more applied in fault-tolerant HSV [20; 21]. A new adaptive nonlinear generalized predictive controller is proposed for the longitudinal dynamics of hypersonic vehicles with unknown parameters and constraints [1], showing a good control effect. Nonlinear generalized predictive control [22] shows the good dynamic performance and hugely decreases the computation burden compared with the usual model predictive control. Nonetheless, since inertial matrix variations are not taken into account, they may end up delivering unacceptable performance for HSV attitude control in the face of an unexpected centroid shift. In [23; 24], a six-order dynamic compensation control law without considering the inertia of HSV is proposed, which provides a modern treatment method for the change of inertia matrix. However, systematic and eccentric moment uncertainties are not taken into account. In conclusion, it is significant and important to study the FTC scheme of a hypersonic vehicle affected by unexpected centrocentric migration, actuator failure and system input saturation. The main contributions are as follows:  
* The topic of pose system modeling of rigid HSV with unexpected centroid shifts and actuator faults is explored in detail. In contrast to the common practice in the FTC literature for actuator failures, the challenge of the proposed FTC design manifests itself in the simultaneous variation of the system inertia matrix, the moment of eccentricity and the strong system uncertainty. * Due to the above-mentioned coupling and unknown adverse effects, a higher-order sliding mode observer in slow-loop and the adaptive estimators are designed by the nature of eccentric moments and system uncertainties and the actuator faults instead of merging them into one item to improve the control performance of the system. * The algorithm uses an adaptive observer and estimator, combined with adaptive feedback control, and can achieve attitude tracking without knowing the inertia matrix \(J\), despite the existence of system inertia matrix, eccentric moment and actuator failures. In addition, the developed FTC scheme has fixed control structure and few design parameters, which is an effective method to solve similar problems. In this paper, we focus on fault-tolerant control of HSV in the presence of unexpected centroids, actuator faults and external disturbances. The paper is organized in the following subsections: Section 2 is devoted to the modeling of HSV with unexpected centroid shifts and the analysis of their properties, nd some details with respect to the process of modeling are delivered in Appendices A and B.