## 2 Model Description of the Saucer-Shaped UAV  
The saucer-shaped UAV studied in this work is an improved version of the previous aerodynamic model mentioned in Ref. [31], as shown in Figure 1. The UAV is composed of a saucer-shaped lifting-body fuselage, two split drag rudders (SDRs) mounted on the trailing edge of each small wing and four tailerons (inboard and outboard). The fuselage is the main part for providing lift and large payload space. The twin wings are designed as pelvic fins to reduce the induced drag and to help maintain lateral stability, instead of providing lift. Based on the control effectiveness of these aerodynamic control surfaces, we reallocate and combine them, which is equivalent to the conventional effectors. The two inboard tailerons (\(\delta_{1L},\delta_{1R}\)) are deflected symmetrically as a whole to provide pitch-control power as a classic elevator, and the deflection angle is denoted by \(\delta_{1 LR}\). The two outboard tailerons (\(\delta_{2L},\delta_{2R}\)) are deflected differentially to provide roll-control power similar to the aileron, of which the deflection angle is denoted by \(\delta_{2 LR}\). The SDRs (\(\delta_{3L},\delta_{3R}\)) are used as a drag-driven effector for yaw control with unilateral SDR operating mode, and the corresponding deflection angle is denoted by \(\delta_{3}\). Figure 1: The saucer-shaped unmanned aerial vehicle (UAV) with multiple control surfaces. The notations of related variables of the UAV are shown in Table 1. This paper mainly focuses on the altitude motion, which can be described by the nonlinear system as follows, similar to the model in Ref. [32]. \[\left\{ \begin{array}{l}\dot{\alpha}=-p\cos\alpha\tan\beta+q-r\sin\alpha\tan \beta-\frac{P\sin\alpha+L-mg\cos\mu\cos\gamma}{mV\cos\beta},\\ \dot{q}=\frac{l_{x}-l_{y}}{l_{y}}pr-\frac{l_{m}}{l_{y}}(p^{2}-r^{2})+\frac{M+ Pl_{p}}{l_{y}},\\ \dot{\mu}=\frac{p(\sin\alpha\cos\gamma+\cos\alpha\sin\beta\sin\gamma)+L\cos \gamma-Y\sin\gamma-mg\cos\mu}{mV},\\ \dot{h}=V\sin\mu,\end{array} \right. \tag{1}\]  
In the longitudinal equation above, the variables for lateral states \(p\), \(r\), \(\beta\) and \(\gamma\) are always very small and thus can be simplified to zero and the expression of flight path angle \(\mu=\theta-\alpha\) approximately holds. Considering the configuration illustrated in Figure 1, when the two inboard tailerons are used as an elevator, since the flow condition changes between the adjacent outboard and inboard tailerons surface, inevitably, interactions within control effectors will be introduced. Moreover, as the tailerons are located just behind SDRs, the downstream flow over these effectors will be disturbed by the SDRs; meanwhile, the deflection of SSDs at different attack angles will additively yield lift effects and cross-axis coupled moments. Based on the analysis above, the expression of aerodynamic-related forces and moments \(L\) and \(M\) are expanded as \(L=QS(C_{L0}+C_{L\alpha}\alpha+\Delta C_{Lb}(\delta_{1 LR},|\delta_{2 LR}|,|\delta _{3}|))\) and \(M=QSc_{A}(C_{m0}+C_{ma}\alpha+(C_{m0}\cdot c_{A}/2V)q+C_{m\infty}\delta_{1 LR} +\Delta C_{m\beta}(|\delta_{2 LR}|,|\delta_{3}|))\), where \(Q=1/2\rho_{h}V^{2}\) is the dynamic pressure and \(C_{L0}\), \(C_{L\alpha}\), \(C_{m0}\), \(C_{ma}\), \(C_{m\beta}\) and \(C_{m\infty}\) denote the aerodynamic derivatives which can be obtained via computational fluid dynamics technique. \(\Delta C_{L\beta}(\cdot)\) and \(\Delta C_{m\beta}(\cdot)\) denote the uncertain terms caused by the coupling of control surface effects and nonlinear factors. Without loss of generality [33], velocity \(V\) is assumed to be a known constant since the focus of this paper is altitude control and flight path angle \(\mu\) is small, i.e., \(\sin\mu\approx\mu\). Furthermore, the related dynamics of the altitude in Equation (1) can be rewritten as  
\[\left\{ \begin{array}{l}\dot{h}=V\mu,\\ \dot{\mu}=f_{\mu}+\varphi_{2}\theta+d_{\mu},\\ \dot{\theta}=q,\\ \dot{q}=f_{\theta,\mu,d}+\varphi_{4}\delta_{1 LR}+d_{q},\end{array} \right.