## 2 Model Description of the Saucer-Shaped UAV
\tag{2}\]  
where \(f_{\mu}=\frac{QS(C_{L0}-C_{L\alpha}\mu)-mg\cos\mu}{mV}\), \(\varphi_{2}=\frac{QSc_{A}}{mV}\) and \(\varphi_{4}=\frac{QSc_{A}C_{m\infty}}{l_{y}}\) can be seen as constant values here and \(f_{\theta,\mu,q}=\frac{QSc_{A}}{l_{y}}(C_{m0}+C_{ma}(\theta-\mu)+C_{mq}\frac{ EQ}{l_{y}}q)\), \(d_{\mu}=\frac{P\sin\alpha}{mV}+\frac{QSc_{A}(\cdot)}{mV}\) and \(\Delta d_{q}\), \(d_{q}=\frac{P\sin\alpha}{Ty}+\frac{QSc_{A}}{l_{y}}\Delta C_{m\beta}(\cdot)+ \Delta d_{q}\), \(\Delta d_{\mu}\) and \(\Delta d_{q}\) stand for parametric uncertainties and external disturbances, etc. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Symbol** & **Variable** & **Symbol** & **Variable** \\ \hline \(m(kg)\) & Mass & \(V(m/s)\) & Velocity \\ \(\mu,\gamma(rad)\) & Flight path angle andbank angle & \(l_{x},I_{y},I_{z},I_{xz}\) & Three principal moments of \\  & & \((kg\cdot m^{2})\) & inertia and the product of inertia \\ \(\alpha,\beta(rad)\) & Angle of attack and sideslip & \(Q(N/m^{2})\) &
\begin{tabular}{c} about the x and z axes \\ Dynamic pressure \\ Atmospheric density \\ \end{tabular} \\ \(p,q,r(rad/s)\) & Roll, pitch and yaw & \(C_{L0},C_{L\alpha}\) & Aerodynamic lift coefficients \\  & angular rate & \(C_{m0},C_{ma}\), \\ \(L,Y,P(N)\) & Lift force, side force and thrust & \(C_{m\mu},C_{m\infty}\) & Aerodynamic pitch coefficients \\ \(M(N\cdot m)\) & Pitch moment & \(S(m^{2})\) & Reference area \\ \(l_{p}(m)\) & Position of the engine in the body axis & \(c_{A}(m)\) & Chord \\ \(g(m/s^{2})\) & Gravitational acceleration & \(h\) & Altitude \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main notations and definitions. For the nonlinear system (2), the main control task is to steer the UAV to stably track a desired altitude with a sufficient small tracking error, under the existence of couple effect of multiple control effectors, internal parametric uncertainties and external disturbances. Additionally, \(d_{\mu}\) in system (2) is the so-called mismatched disturbance/uncertainty that should be dealt with. To guarantee that the control task is achievable, the following assumption is invoked. **Assumption 1:**_The compound disturbances \(d_{\mu}\) and \(d_{q}\) and the corresponding derivatives are bounded, namely there exist positive constants \(M_{\mu}\), \(N_{\mu}\), \(M_{q}\) and \(N_{q}\) satisfying that \(\left|d_{\mu}\right|\leq M_{\mu}\), \(\left|\dot{d}_{\mu}\right|\leq N_{\mu}\), \(\left|d_{q}\right|\leq M_{q}\) and \(\left|\dot{d}_{q}\right|\leq N_{q}\). The first and second time derivatives of the desired altitude reference \(h_{d}\) exist and are bounded._  
**Remark 1:**_The assumption above about disturbance is fairly reasonable, which also has been widely applied all along in the existing literature on ESO-based control and disturbance rejection control [29; 30; 34]. Specifically, the un-modelled coupled nonlinearity and unknown uncertainties are affected by the flight environment and aircraft effectors structure parameters, which can only change continuously and smoothly. Therefore, the internal uncertainty and its derivatives are bounded. On the other hand, the main causes of external perturbation include complex temperature and pressure changes, wind gusts disturbances, etc. As for a practical physical system, external interference and its time derivatives are obviously limited._