## 6 Simulation Experimental Results  
In this paper, MATLAB 2018a simulations were divided into two parts. The first used the actual parameters of urban rail trains to carry out the RBFNN position output-constrained robust adaptive control (RBFNN-POCRAC) design and desired curve tracking. Then, with the same train parameters and desired curve, the position output-constrained robust adaptive control (POCRAC) without RBFNN approximation of additional resistance and unknown disturbance, using the PID controller and the RBFNN-PID controller in the literature [30], was selected for performance comparison. The desired speed and position curve of the train tracking target is shown in Figure 3. The parameter information of the train route such as the slope and curve radius is shown in Table 1. Equation (4) was selected as the train dynamics model. The basic resistance simulation parameters were set as \(a^{*}=0.3\), \(b^{*}=4\times 10^{-3}\), \(c^{*}=1.6\times 10^{-4}\). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Range** & **Value** \\ \hline \multirow{8}{*}{Slope/(\%)} & 0–3800 & 2 \\  & 3800–9200 & \(-1.5\) \\  & 9200–21,400 & 0 \\  & 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 \\ \hline \multirow{8}{*}{Curve (m)} & 0–4600 & 1000 \\  & 4600–18,000 & 1200 \\ \cline{1-1}  & 18,000–24,200 & 800 \\ \cline{1-1}  & 24,200–29,300 & 1500 \\ \cline{1-1}  & 29,300–34,000 & 700 \\ \cline{1-1}  & 34,000–48,000 & 1300 \\ \cline{1-1}  & 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. Figure 3: Desired speed and position profiles of train operation. Figure 6: Speed tracking performance. Figure 7: Speed error. It can be seen from Figure 4 that the position tracking curve was closely attached and there was no system overshoot phenomenon, indicating that the tracking effect of the controller was good. At the same time, it can be seen from Figure 5 that, under the system model parameters and complex route conditions of the train operation, the results could converge quickly, and the position signal was bounded, thus identifying the given train position curve with high precision. When the train operated on a route with a large slope and complex curve, the control accuracy of RBFNN-POCRAC controller decreased due to the strong additional resistance and external interference, but the position tracking error was still less than 0.2 m, thus meeting the requirements of train parking accuracy. Therefore, the RBFNN-POCRAC controller not only ensures the stable operation of the train on the route with a large slope and complex curve, but also achieves a final parking accuracy of almost 0, thereby meeting the control requirements. According to the speed tracking performance in Figure 6 and the speed tracking error in Figure 7, when the initial speed was 0, the controller could track the given train speed curve with small error, and the speed signals were bounded. When the train was operating on a complex route with a large slope and smaller curve radius, the speed tracking fluctuated due to the strong disturbance from the outside, and the speed error was \(-0.24\) m/s to 0.26 m/s, but the speed tracking error of the remaining routes was almost zero. Therefore, the RBFNN-POCRAC algorithm proposed in this paper can ensure the safety of train operation. Figure 8 shows the train control input curve of the RBFNN-POCRAC algorithm, i.e., the acceleration curve of train operation. When the train started, it needed to overcome its own gravity and other unknown disturbances, and the maximum acceleration value was \(0.48\) m/s\({}^{2}\). When the train was operating from 52 s to 248 s, in order to overcome the interference of the slope and curve, the controller quickly switched the control input to maintain the control accuracy.