## 1 Introduction
However, the standard backstepping algorithm has the inherent disadvantage of an \"explosion of terms\" caused by the repeated differentiations of virtual controllers. To eliminate the drawback of classical backstepping, dynamic surface control technique combined with adaptive neural networks [17] or fuzzy logic systems [18] were put forward for a class of uncertain nonlinear systems with external disturbances. On the other hand, the command filtered backstepping method [19; 20] was investigated to alleviate the calculation burden, in which complex error compensation mechanism (ECM) should be designed to ensure control performance. Compared with the asymptotic control approach, the finite time control technique has the advantages of faster response, higher tracking precision and better disturbance-rejection ability. [PERSON] et al. [21] addressed a novel composite backstepping framework, where finite-time convergence property is guaranteed by introducing the fractional power functions of tracking errors and the finite-time filters of intermediate command signals. In [22], the first-order Levant differentiator has been applied to each step of the backstepping, which can approximate the derivative of the virtual control in finite-time. In industrial applications, the extended state observer (ESO) technique has been attracting intensive attention, as it can simultaneously estimate the internal uncertainty (parameters or structure) and external disturbance in real time even in the absence of an accurate mathematical model of the system [23; 24]. Successful applications include mechatronics systems [25], hydraulic system [26], quadrotors [27], autonomous driving [28], etc. [PERSON] et al. [29] firstly explored a generalized extended state observer (GESO) for multi-input-multi-output systems with nonintegral-chain form and mismatched disturbances/uncertainties. [PERSON] et al. first conducted the theoretical analysis of nonlinear ESO in [30]. The study provided a rigorous proof of the convergence of high-gain nonlinear ESOs for one kind of nonlinear system with large uncertainty both from internal and external disturbances. Nevertheless, high observer gain will give rise to the peaking phenomenon, which may deteriorate transient performance. According to the foregoing researches, a novel differentiator-based backstepping control scheme combined with a nonlinear ESO for a saucer-shaped BWB UAV subject to both matched and mismatched nonvanishing disturbances/uncertainties is proposed and carried out in this paper. Compared with the existing research, the main contribution of this paper is therefore threefold:  
1. The problem of \"explosion of terms\" is eliminated by employing a finite-time-convergent second-order differentiator, which can not only precisely filter the virtual control command and obtain their differential signals but also guarantees the finite-time stable property. 2. To achieve the precise altitude controller design, a nonlinear ESO is proposed to estimate and compensate the total effect of parametric uncertainties, un-modelled dynamics and external disturbances in real time by viewing them as an extended state of the system. The nonlinear gain function alleviates the peaking value problem and improves observer performance. 3. A differentiator-based composite backstepping control framework integrated with the ESO technique is developed, along with a detailed stability analysis of the whole closed-loop structure. The proposed control scheme of the saucer-shaped BWB UAV fills in the gaps of related researches on aircrafts with innovative configurations. In what follows, Section 2 will provide the mathematical model of the saucer-shaped UAV and the related problem description. In Section 3, the composite differentiator-based backstepping controller combined with a nonlinear ESO will be proposed. Then, the stability analysis will be given in Section 4. Section 5 will present the simulation results, which demonstrate the effectiveness of the proposed approach.