## 5 Simulation Experiment  
In order to verify the effectiveness of the proposed control algorithm, MATLAB 2018a simulation results are given in this paper. The control effects of ATSM-FTC without RBFNN and ATSM-FTC-RBFNN are compared. In the simulation model, the train operating route length is 53.88 km, the train operating time is 2000 s, and the desired position and speed curve of train tracking are shown in Figure 3. The parameter information of train routes such as slope and curve are shown in Table 1.  
Figure 3: Desired speed and position profiles of train operation. In the simulation environment, the delay of the speed sensor is set as \(\tau=1.5\), the input saturation is quantified as the upper limits of acceleration \(u^{+}=1.5\), and the lower limits of deceleration \(u^{-}=1.5\). The basic resistance simulation parameters are set as \(a^{*}=0.3\), \(b^{*}=4\times 10^{-3}\), \(c^{*}=1.6\times 10^{-4}\). The structure of RBFNN is 2-5-1, \(\chi=0.2\), \(\alpha=0.04\). The control parameters are set as \(\beta=0.05\), \(p=13\), \(q=11\), \(k=30\), \(\eta=0.4\), \(\lambda_{1}=0.01\), \(\lambda_{2}=0.01\), \(\lambda_{3}=0.01\), \(\sigma_{1}=0.005\), \(\sigma_{2}=0.005\), \(\sigma_{3}=0.005\), \(\sigma_{4}=0.001\), \(\Gamma=diag[0.1]\), \(\gamma=0.01\), \(\varpi=0.002\). When the simulation time is greater than or equal to 5, take \(\delta=0.2\). The initial state is selected as \(x_{1}(0)=0\), \(x_{2}(0)=0\), \(\dot{a}=0.3\), \(\dot{b}=0\), \(\dot{c}=0\), and \(\dot{\delta}=0.2\). For the given curve of train desired position and desired speed, Figures 4 and 5 respectively show the performance diagrams of position tracking and speed tracking of ATO control algorithm based on ATSM-FTC-RBFNN. It can be seen from Figures 4 and 5 that the ATSM-FTC-RBFNN algorithm has good tracking performance and can realize high-precision tracking of the desired position and speed curve. According to the enlarged diagram shown in Figure 4, it can be seen that the position tracking error of the control algorithm at the parking point is \(-2\) mm. According to the enlarged diagram shown in Figure 5, when the control algorithm approaches the parking position, the speed tracking error gradually decreases and finally approaches zero. Therefore, the ATSM-FTC-RBFNN control method can achieve high-precision tracking of train desired position and speed curve, and the position signal and speed signal are bounded under the conditions of input saturation limit, speed delay, actuator failure, uncertain Davis equation coefficient of basic resistance, and additional resistance disturbance. As shown in Figure 6, the position error of ATSM-FTC-RBFNN is the largest when the train is just started. With the normal operation of the train for 630 s, the position tracking error is reduced to zero. In the process of train operation, due to the influence of the uncertainty of Davis equation coefficient of basic resistance and the interference of route additional resistance, the position tracking error increases negatively to \(-0.155\) m in 1148 s, and then increases continuously. After 96 s, the position error increases to 0.13 m and then decreases continuously. The final parking accuracy is \(-2\) mm. Although the position tracking error of train operation changes continuously, the position control accuracy at any time is less than \(\pm 0.2\) m, which meets the requirements of accurate train control. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Range** & **Value** \\ \hline  & 0–3800 & 2 \\  & 3800–9200 & \(-1.5\) \\  & 9200–21,400 & 0 \\ Slope/(\%\({}_{\text{o}}\)) & 21,400–23,900 & 5 \\  & 23,900–29,900 & 2.5 \\  & 29,900–32,300 & \(-3\) \\  & 32,300–50,000 & 0 \\  & 50,000–53,880 & 1.2 \\  & 0–4600 & 1000 \\  & 4600–18,000 & 1200 \\  & 18,000–24,200 & 800 \\ Curve (m) & 24,200–29,300 & 1500 \\  & 29,300–34,000 & 700 \\  & 34,000–48,000 & 1300 \\  & 48,000–53,880 & 1200 \\ \hline \hline \end{tabular} The additional resistance caused by the route condition.  
\end{table} 
Table 1: Parameters for route condition.