## 5 Simulations and Results
### Performance Evaluation and Discussion  
The simulation results are assessed using the following key performance metrics (KPIs). * \(RMSE_{\theta}\): The root mean squared value of the tracking error \(e_{\theta}\), calculated as follows: \[RMSE_{\theta}=\sum\sqrt{\frac{\left(e_{\theta}(n)\right)^{2}}{n}}\] (35) where \(n\) represents the total number of samples. * OS: The peak deviation observed during the start-up phase of the response;
* \(T_{\text{sgt}}\): The duration required for the system response to settle within \(\pm\)2% of the reference value;
* \(M_{\text{peak}}\): The maximum deviation (overshoot or undershoot) that occurs following a disturbance;
* \(T_{\text{rrc}}\): The time taken for the response to stabilize within \(\pm\)2% of the reference value after experiencing a disturbance. Table 2 presents a quantitative summary of the simulation results, demonstrating the robust tracking and disturbance rejection capabilities of the proposed control law. The results validate that the proposed RLCA robustifies control performance by ensuring a balanced trade-off between aggressive and conservative control actions, improving transient response, and preserving steady-state accuracy. In Test A (Figure 9), the LQI controller exhibits moderate tracking performance, characterized by noticeable overshoot, oscillations, and an extended settling time. In contrast, the RLCA scheme achieves superior tracking accuracy, with minimal overshoot, faster convergence, and reduced steady-state fluctuations. In Test B (Figure 10), the LQI controller maintains an oscillatory tracking response and demonstrates sensitivity to sinusoidal disturbance, resulting in lag and noticeable degradation in tracking accuracy. Meanwhile, the RLCA scheme exhibits greater robustness and adaptability to track the ramp trajectory, while also optimizing control resource allocation. In Test C (Figure 11), the LQI-controlled system shows noticeable deviations from the reference trajectory, followed by a slow recovery. In contrast, the RLCA scheme effectively dampens impulsive disturbances, quickly restoring the system to its reference position while also attenuating peak overshoots. In  
Figure 14: Ramp reference tracking response of the UAV under impulsive disturbances. Test D (Figure 12), the LQI controller struggles to maintain steady-state accuracy after a disturbance and exhibits a slower transient recovery. However, the RLCA scheme achieves superior trajectory tracking accuracy by efficiently adapting to the step disturbance. In Test E (Figure 13), the LQI controller demonstrates poor model error compensation, with large fluctuations in the response. Conversely, the RLCA scheme significantly improves disturbance attenuation, resulting in a smoother response. Similarly to payload variations, the changes in actuator dynamics also impact the UAV's state-space model by modifying key system parameters. While actuator variations alter control effectiveness, payload changes affect stability derivatives. However, both of these parametric uncertainties influence the UAV's overall flight behavior. Since both scenarios lead to variations in UAV's system dynamics, the outcomes of Test E validate that RLCA's adaptive control strategy remains effective in compensating for such uncertainties in real time. In Test F (Figure 14), the LQI controller exhibits noticeable chattering and sensitivity to disturbances in the tracking response, leading to increased tracking error and slower stabilization. Specifically, it demonstrates higher \(RMSE_{\theta}\), peak deviations, and recovery times, resulting in lag and reduced accuracy. Meanwhile, the RLCA scheme significantly enhances robustness and adaptability, effectively minimizing tracking error, overshoot, and transient recovery time. By adaptively regulating the control resource allocation, the RLCA scheme ensures improved disturbance rejection and faster transient recovery, making it a superior alternative to the LQI controller.