## 5 Simulation Results  
Table 1 illustrates the dimensions of the powered parafoil investigated in this paper. Numerical simulations were performed in the Matlab environment and executed on a laptop with an i7-10875H CPU. In addition, the hyperparameters involved in the TD3 algorithm were \(\gamma=0.99\) and \(\tau=0.005\). The simulation in this paper was completed on the MATLAB platform. The learning rate of networks was 0.001. To validate the efficacy of the proposed TD3-LADRC method, simulation verification is performed using the model presented in Section 2. With an initial velocity of the parachute set as \(V_{0}=\left[14.9,0,2.1\right]^{T}\) m/s and \(W_{0}=\left[0,0,0\right]^{T}\) rad/s, the initial position is specified as  
Figure 5: Structure diagram of critic and actor networks. \((x_{0},y_{0},z_{0})=(20,20,550)\) m. The initial Euler angles are defined as \([\phi_{0},\theta_{0},\psi_{0}]=[0,0,0]\). In addition, suppose the following formula expresses the target trajectory:  
\[ \begin{cases}x_{d}(\varpi)=6\varpi\\ y_{d}(\varpi)=8\varpi\\ z_{d}=500\end{cases}  \tag{33}\]  
Subsequently, the TD3-LADRC control method is employed to achieve the desired trajectory, as depicted in Equation (33). In the control system, the parameter values in the guidance law are set as \(\alpha=0.02\) and \(k=50\). For the horizontal trajectory controller, \(\omega_{o}\) and \(b_{0}\) are chosen as 5 and 0.5, respectively. Likewise, for the altitude controller, the values selected are 15 and 2, respectively. Furthermore, the action space is expressed by Equation (34). Moreover, the following four cases are considered:  
* Wind-free: there is no wind during the flight;
* Wind-X: a wind of 2 m/s from the west direction is added at 60 s and lasts until the end of the simulation;
* Wind-Y: a wind of 2 m/s from the south direction is added at 60 s and lasts until the end of the simulation;
* Wind-Z: a wind of 2 m/s from the vertical direction is added at 60 s and lasts until the end of the simulation. \[ \begin{cases}k_{p1}\in[0.005,0.05]\\ k_{d1}\in[0.1,0.5]\\ k_{p2}\in[0.05,0.5]\\ k_{d2}\in[1,2]\end{cases}  \tag{34}\]  
The simulation results are shown in Figures 6-11. First and foremost, the results of episode rewards are displayed in Figure 6, which indicate that the TD3 agent can achieve stabilization. For the four cases mentioned above, Figure 7 displays the schematic diagrams of both the 3D and 2D trajectories. Additionally, Figure 8 illustrates the progression of the steering gear and thrust obtained by the controller. The corresponding trajectory tracking errors and the reward value change process are depicted in Figure 9. Furthermore, Figure 10 showcases the variations in Euler angles and velocity throughout the flight, while Figure 11 presents the TD3-optimized controller parameters. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter Description** & **Value** \\ \hline Wing span & 4.5 m \\ Mean aerodynamic chord & 1.3 m \\ Mass of parafoil & 1.7 kg \\ Mass of payload & 20 kg \\ Wing area & 6.5 m\({}^{2}\) \\ Rope length & 3 m \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Physical parameters of the powered parafoil system. Figure 8: Control variables. Figure 6: Episode reward for the TD3 agent. Figure 7: Trajectory performance in different cases. Figure 9: Trajectory tracking errors and the corresponding reward value. In general, our objective is to test the trajectory tracking effect of the proposed TD3-LADRC in various cases. Additionally, we compared the control effect of the LADRC with fixed parameters in the obtained results. For the fixed parameters, we selected \(k_{p1}=0.005\), \(k_{d1}=0.1\), \(k_{p2}=0.05\), and \(k_{d2}=1\). Overall, the method depicted in the results diagram can successfully accomplish trajectory tracking control. This, to a certain extent, demonstrates the effectiveness of the proposed guidance law and LADRC control method.