## 4 Comprehensive Simulation on UAV Landing Scenario
Similar results regarding the tracking performance of the airspeed trajectory are shown in Figure 3. Notice that the excessive relaxation of the performance envelope during the transient period is owing to the heavily saturated control input as depicted in Figure 4a. Nevertheless the predefined performance characteristics are readily recovered at the steady state as is shown in Figure 3a. Thus, the airspeed tracking error is practically converging to zero as it can be observed in Figure 3b. The actual amplitude and rate constrained throttle setting \(\delta_{T}(t)\) is illustrated in Figure 4a along with the unconstrained (desired) one \(u_{d}(t)\). Notice that the actual control input is much smoother than the desired one, owing to the rate limitation visualized in  
Figure 3: (**a**): The evolution of airspeed tracking error \(V(t)-V_{d}(t)\) (orange line) within the adaptive performance envelope delimited by \(p_{2}(t)\) and \(-p_{2}(t)\) (black lines), conventional PFs are denoted by dotted lines. (**b**): The evolution of the actual airspeed \(V(t)\) (purple line) vs. the reference velocity \(V_{d}(t)\) (dotted line). Figure 2: (**a**): The evolution of altitude tracking error \(h(t)-h_{d}(t)\) (orange line) within the adaptive performance envelope delimited by \(p_{1}(t)\) and \(-p_{1}(t)\) (black lines), conventional PFs are denoted by dotted lines. (**b**): The evolution of the actual altitude \(h(t)\) (purple line) vs. the reference altitude \(h_{d}(t)\) (dotted line). Figure 6 illustrates the wind gusts responsible for inducing chattering in the desired control input \(u_{d}(t)\). It is worth noting that the proposed control scheme effectively moderates the effects of these disturbances by imposing a rate limit on the control signal. This ensures a smooth and stable response, as demonstrated in Figure 4a. Figure 4: **(a)**: The evolution of the actual throttle setting \(\delta_{T}(t)\) (orange line) vs. the reference, unconstrained control signal \(u_{d}(t)\) (black line), amplitude limit (\(\delta_{T}\)) is denoted by blue dotted line. **(b)**: The evolution of the unconstrained control signal \(\delta_{e}(t)\) (black line) vs. the corresponding amplitude limit (\(\delta_{e}\)) (blue dotted line). Figure 5: The unconstrained (desired) elevator deflection \(\delta_{e}(t)\) is also depicted in Figure 4b. Note that the actual elevator deflection is obtained by \(\sigma(\delta_{e}(t),\bar{r})\). At the 10 th second of the simulation, the elevator deflection saturates quickly in order to preserve the adaptive constraints. In particular, notice that in Figure 7 the performance boundaries of the state tracking errors \(e_{\gamma}(t),e_{\theta}(t),e_{q}(t)\) fluctuate as the sudden occurrence of wind induce perturbations to the closed-loop system. Nevertheless, the prescribed performance characteristics are exponentially recovered and the predefined state constraints are satisfied as shown in Figure 8. More specifically, Figure 8 depicts the evolution of the actual constrained states \(\gamma(t),\theta(t),q(t)\) versus the corresponding unsaturated reference trajectories, generated by the proposed control scheme. It is worth mentioning that the performance relaxation that leads to the trade-off among input, output, and state constraints is highly affected by the coupling between the constrained states and inputs of the UAV. Figure 6: (**a**): The velocity of the wind along with the horizontal axis. (**b**): The acceleration of the wind along with the horizontal axis. (**c**): The velocity of the wind along with the vertical axis. (**d**): The acceleration of the wind along with the vertical axis. Figure 7: (**a**): The evolution of flight-path angle tracking error \(e_{\gamma}=\gamma(t)-\gamma_{d}(t)\) (orange line) within the adaptive performance envelope delimited by \(p_{3}(t)\) and \(-p_{3}(t)\) (black lines). (**b**): The evolution of pitch angle tracking error \(e_{\theta}=\theta(t)-\theta(t)\) (orange line) within the adaptive performance envelope delimited by \(p_{5}(t)\) and \(-p_{5}(t)\) (black lines).