## 1 Introduction  
The powered parafoil is a prevalent new type of air vehicle with a flex wing [1, 2]. Because the engine is equipped with the payload, compared with traditional parafoils, the powered parafoil not only can glide but also cruise and climb, which traditional parafoils cannot perform [3, 4, 5]. The powered parafoil has been applied to paragliding sports, supply airdropping, pesticide spraying, and airport demisting, to name but a few, due to its excellent maneuverability [6]. In recent years, the control of powered parafoils has become a research hotspot. Compared with the horizontal control of traditional parafoils, the altitude control of powered parafoils has received extensive attention and has been a challenge because of its complex aerodynamics characteristics. Many strategies have been proposed to control the altitude of powered parafoils. [PERSON] et al. analyzed the flight performance of altitude control and derived the longitudinal model of a powered parafoil [7]. [PERSON] and [PERSON] designed a nonlinear control law for a powered parafoil based on partial feedback linearization to track a desired trajectory in the longitudinal plane [8]. [PERSON] et al. presented a precise-gain method to handle the problem of longitudinal motion control of a powered parafoil [9]. The backstepping control was first employed to control the altitude of a powered parafoil using its lateral model [10]. Then, a fuzzy backstepping control was extended to improve the control performance of the altitude control based on a variable-gain scheme [11]. [PERSON] et al. proposed an altitude-tracking control method for a powered parafoil using the coefficient adaptive control and the characteristic model of the parafoil [12]; however, the specification of the guidance was not provided. [PERSON] al. presented a spatial path-tracking control of a powered parafoil using the guidance theory combined with the linear active disturbance control (LADRC) [13]. The above-mentioned methods mainly used a simplified model of powered parafoils to design a controller. However, this may impose limitations on control performance as there exist strong nonlinearities and complex model couplings in powered-parafoil systems. Although [PERSON] and [PERSON] employed methods of the characteristic model and LADRC that do not rely on the precise model of a powered parafoil to remove the limitations, it increases the complexity of the system design and brings difficulty in analyzing the stability of control systems. The sliding mode control (SMC) is a commonly used method for the aircraft [14; 15]; however, the control is susceptible to system uncertainties and disturbances. How to effectively suppress disturbances and improve the robustness of a control system is one of the key points in system design [16; 17]. On the other hand, the fractional-order theory [18; 19] is widely used in industrial control systems. A fractional calculus operator shows good robustness for systems with uncertainties and external disturbances due to its hereditary and memorability. This paper presents an alternative way to address the problem of the altitude control of a powered parafoil using the fractional sliding-mode backstepping control combined with a linear extended state observer (LESO). First, the inclination angle model of a powered parafoil is derived according to the guidance law. The altitude control of the powered parafoil is converted into the issue of the inclination angle control. Then, an LESO is used to estimate system uncertainties and exogenous disturbances. A fractional dynamic sliding-mode surface is introduced into the backstepping control to improve the transient performance of the altitude tracking. A stability criterion is derived to guarantee that virtual control variables and the error of system states are bounded. Finally, the validity of the presented method is demonstrated by simulation results of an 8-degree-of-freedom powered parafoil. The rest of the paper is organized as follows.