## 4 Comprehensive Simulation on UAV Landing Scenario  
In this section, we demonstrate the effectiveness of the proposed controller by conducting a simulation study using an Aerosonde UAV, as described in [33]. The objective is to guide the UAV in tracking a predetermined reference trajectory for landing, while accounting wind disturbances, predefined input constraints as well as adaptive prescribed performance output and state constraints. The aerodynamic longitudinal coefficients of the Aerosonde model are presented in Table 2, whereas the parameters of the control scheme are outlined in Table 3. It is worth noting that the throttle settling limit is intentionally set at 65% to showcase the proposed controller's ability to handle performance specifications alongside input limitations. Moreover, Remark 2 emphasizes that the task of selecting the gains is straightforward, hence all control gains \(k_{i}\) are uniformly set to validate this claim. The reference landing trajectory is defined as \(h_{d}(t)=100\frac{\exp(-0.07t)-1}{\exp(-0.07t(-100))+1}+100\) and the airspeed profile is chosen as \(V_{d}(t)=50-5\sin\left(0.0038t\right)\). Furthermore the initial state conditions are selected as \(x(0)=[95,45,0.04,0.03,0,0]^{T}\) and the initial values of the adaptive performance functions are set to \(p_{1}(0)=6.75,p_{2}(0)=5.5,p_{3}(0)=0.12,p_{4}(0)=0.13,p_{5}(0)=0.2,p_{6}(0)=1.65\). Finally, in order to demonstrate the robustness of the proposed control scheme, we induce wind gusts \(w_{x}(t)=1.5\sin\left(0.0335t\right)\), \(w_{h}(t)=2\cos\left(0.05t\right)\), \(\forall t\in[10,104.25]\) for a simulation period of 200 s.  
The adaptive prescribed performance of the altitude tracking error is depicted in Figure 2a, where the proposed PFs create an adaptive performance envelope within which the tracking error is evolving. Note that the conventional PFs are denoted by dotted-lines and as one can see the performance specifications are relaxed at the time instant the wind starts affecting the dynamics of the system, in order to maintain the altitude tracking error strictly inside the performance envelope when the output constraints are conflicting with the input and state saturation, i.e., the altitude variation rate is delimited by the saturated control effort applied by the actuators. The latter is also affected by the maximum absolute value of flight-path angle, angle-of-attack and pitch rate that are imposed by our control \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multirow{2}{*}{**Value**} & **Longitudinal** & **Value** \\  & & **Coefficient** & **Value** \\ \hline \(m\) & \(13.5\) kg & \(C_{L_{0}}\) & \(0.28\) \\ \(l_{yy}\) & \(1.135\) kg m \({}^{2}\) & \(C_{L_{u}}\) & \(3.45\) \\ \(S\) & \(0.55\) m\({}^{2}\) & \(C_{L_{u}}\) & \(-0.36\) \\ \(c\) & \(0.18994\) m & \(C_{D_{0}}\) & \(0.03\) \\ \(C_{prop}\) & \(1\) m\({}^{2}\) & \(C_{D_{s}}\) & \(0.3\) \\ \(S_{prop}\) & \(0.2027\) m\({}^{2}\) & \(C_{M_{0}}\) & \(-0.0238\) \\ \(\rho\) & \(1.2682\) kg/m\({}^{3}\) & \(C_{M_{0}}\) & \(-0.38\) \\ \(k_{m}\) & \(80\) & \(C_{M_{0}}\) & \(-3.6\) \\ \(g\) & \(9.8\) & \(C_{M_{o}}\) & \(-0.5\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Aerodynamic coefficients. \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{1}{c}{**Parameter**} & **Value** \\ \hline \(k_{i}\), \(i\in\{h,v,\gamma,\theta,q,r\}\) & \(2\) \\ \(\lambda_{i}\), \(i\in\{h,v,\gamma,\theta,q\}\) & \(0.5\) \\ \(\lambda_{r}\) & \(20\) \\ \(p_{\infty}^{i}\), \(i\in\{1,2,4\}\) & \(0.05\) \\ \(p_{\infty}^{i}\), \(i\in\{3,5,6\}\) & \(0.005\) \\ \(\delta_{T}\) & \(0.65\) \\ \(r\) & \(0.25\) \\ \(\delta_{e}\) (\(rad\)) & \(0.2\) \\ \(\gamma\) (\(rad\)) & \(0.06\) \\ \(\tilde{\theta}\) (\(rad\)) & \(0.1\) \\ \(\tilde{q}\) (\(rad\)) & \(0.1\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Control Scheme parameters. scheme, in order to ensure the safety of landing procedure. Additionally, the performance of UAV's altitude versus the reference landing trajectory is depicted in Figure 2b.