Adaptive Sliding Mode Control via Backstepping for an Air-Breathing Hypersonic Vehicle Using a Double Power Reaching Law  
[PERSON]  
1 College of Automation Engineering, Nanjing University of Aeronautics and Astronautics,
restriction and aerodynamic uncertainties by the authors of [30]. In the controller design of AHVs, [PERSON] et al. in 2020 proposed an adaptive backstepping sliding mode scheme for the altitude subsystem [31]. In the literature [32], the backstepping method combined with the neural network was adopted for attitude tracking control of re-entry hypersonic vehicles. In the process of backstepping design, the differential calculations of virtual control laws lead to the \"explosion of complexity\", which can be eliminated by a dynamic surface control approach [33]. In terms of input constraints and uncertainties surrounding AHV design, [PERSON] et al. in 2017 adopted an adaptive backstepping controller for the altitude subsystem to ensure the performance of tracking control [34]. Considering strong uncertainties in AHVs, a more robust performance is important to the AHV controller. Sliding mode control (SMC) is a robust and reliable method, which is widely used in the motion control system of AHVs. The quasi-continuous high-order sliding mode controller was proposed, and then the attack angle and flight path angle were estimated by the high-order sliding mode observer, which can achieve good robust performance in altitude and velocity tracking [35]. [PERSON] et al. proposed a continuous sliding mode controller in 2015, and combined it with a disturbance observer to eliminate the chattering, which can achieve a faster convergence velocity and better robustness [36]. Furthermore, by combining with a finite time observer based on the super-twisting algorithm, an improved sliding mode control was proposed to ensure rapid tracking of the system trajectory [37]. In sliding mode control, the reaching law has a direct influence on the convergence time and stability of the system. The early reaching law adopted a simple sign reaching law. Since it is discontinuous at the origin, when the system converges to the position near the sliding mode surface, repeated switch would lead to chattering of the sliding mode surface. Then, several reaching laws were proposed. In the literature [38], an improved exponential reaching law was proposed, which reduced the chattering of the control input and ensured high tracking performance. A novel power reaching law was proposed by [PERSON] et al., which achieved the high convergence rate compared with the conventional reaching laws [39]. [PERSON] et al. proposed a new approach base on nonsingular fast terminal sliding-mode control to solve fault-tolerant control, and ensure that the system states converge within a finite time [40]. [PERSON] et al. proposed a novel double power reaching law to settle down the chattering and achieve faster convergence [41]. Adaptive ability is also important in designing controllers in terms of uncertainties, and can improve the robust performance of the controller. [PERSON] et al. designed a robust slide surface, and proposed an adaptive sliding controller based on tracking error, which could reduce the influence of uncertainties and disturbances on system [42]. A controller, combining the adaptive terminal sliding mode control method with a novel nonlinear disturbance observer, was proposed by [PERSON] et al. in 2017, and it can achieve good robust performance under uncertainties and disturbances [43]. In the literature [44], [PERSON] et al. proposed a novel disturbance-based adaptive sliding mode control method, which combined an adaptive sliding mode controller with extended observer to obtain good tracking performance. Combining the advantages of backstepping and that of SMC, a new adaptive SMC method is adopted in this paper to reduce the effect of mismatched uncertainties on AHVs. The contributions of this paper are summarized as follows:  
1.