# Data-Driven Model-Free Adaptive Sliding Mode Control Based on FFDL for Electric Multiple Units
## 5 Conclusions  
In this paper, an improved MIMO-FFDL-MFASMC method is proposed for the automatic driving system of high-speed EMUs. In this method, the operation process of the EMUs is equivalent to a full format dynamic data model, and a model-free adaptive controller is designed based on the data model. Then, to reduce the influence of measurement disturbance and improve the robustness of the system, a discrete sliding mode control algorithm is introduced. Furthermore, to prevent the sliding mode control input from being too large, the parameter estimation error is introduced as an additional correction term of the algorithm. The simulation results demonstrate that compared with MFAC and DITSMC, the MFASMC control scheme:  
1. Achieves higher precision tracking control than the traditional MFAC method for given speed-displacement curve, and the error range is between [\(-0.251\) km/h, \(0.206\) km/h], which meets the requirements of train speed error and achieves safe and punctual operation of the train;
2. The control force changes more smoothly, and the acceleration range of each power unit is [\(-0.942\) m/s\({}^{2}\), \(0.858\) m/s\({}^{2}\)], which meets the comfort requirements of passengers;
3. It has a strong suppression effect on external disturbances and good robustness. In conclusion, the speed tracking effect of each power unit of the control algorithm in this paper is favorable, the control force changes smoothly, the acceleration meets the driving safety requirements, and has a strong inhibitory effect on external disturbances. Further, based on this paper, the author will do the following research:  
1. The heavy-haul combined trains composed of different types of locomotives and the delay are considered as [31];  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Methods** & **MSE** & **IAE** & **MAXA** \\ \hline MFASMC & 0.052 & 437 & 0.942 \\ MFAC & 0.248 & 1180 & 1.045 \\ DITSMC & 0.476 & 2810 & 1.056 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of several performance indexes of each control method.  
Using the intelligent control method to optimize the parameters designed by the control method in this paper as [32];
* The heat of multi-agent formation control has been high in recent years, and it aims to accomplish the task efficiently through the collaboration of each agent in the system [33; 34], so the authors will study the model-free adaptive control of high-speed trains with multi-agent in the future;
* Design an algorithm to improve train operation safety [35].  
Conceptualization, L.Z. and Z.L.; methodology, L.Z.and Z.L.; software, L.Z.; validation, H.Y., Y.F. and Y.Y.; formal analysis, Y.Y.; resources, H.Y.; writing--original draft preparation, L.Z.; writing--review and editing, L.Z., Z.L. and Y.F; supervision, H.Y.; funding acquisition, Z.L. and Y.F. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Natural Science Foundation of China (52162048), Training Program for Academic and Technical Leaders of Major Disciplines of Jiangxi Province (20213 BCJ22002) and Natural Science Foundation Project of Liaoning Province (2022-KF-21-03).  
Not applicable.  
The authors declare no conflict of interest.