# Adaptive Cooperative Control of Multiple Urban Rail Trains with Position Output Constraints
## 5 Conclusions  
In this paper, the cooperative operation control schemes for a class of nonlinear urban rail transit train systems are studied, and two position output-constrained adaptive control methods based on multi-agent collaboration are proposed. A set of orderly running urban rail trains are considered as a multi-agent system. The position output constrained adaptive learning controller uses the data of the train itself as well as the neighboring trains to enable the position and speed of each train to track the desired position and speed trajectory of the train. Among them, the train position errors of the two MTCC algorithms with POC meet  
Figure 14: Speed tracking error curves of PID controller. Figure 13: Position tracking error curves of PID controller. the stopping accuracy of less than 0.2 m, respectively, and the position tracking error of their tracking trains is not affected by the position error of the preceding trains and gradually approaches 0, which ensures the stability of the multiple trains tracking operation. The introduction of the potential function ensures that the separation distance between any two neighboring trains is always kept within the designed safety range, which can be flexibly adjusted according to the conditions of train braking distance, safety redundancy distance, train length, and operation interval. The two position output constrained adaptive control methods based on multi-agent cooperation proposed in this paper can not only ensure the tracking operation safety of multiple urban rail trains, but also flexibly adjust the train operation interval and effectively improve the operation efficiency of urban rail system. In particular, single-value learning adaptive cooperative control method with POC for the multiple trains requires only one online parameter adjustment, which guarantees the engineering practicality of the algorithm while ensuring the lowest structural complexity of the MTCC algorithm which will promote the practicability of the theoretical work related to urban rail cooperative control. Additionally, the designed method is also suitable for irregular event interference in a certain range. Although this paper has conducted in-depth research on the cooperative control problem and the model uncertainties problem for multiple urban rail trains, and achieved phased results, the cooperative control problem for the adjustment of urban rail trains' operation status still needs further study due to the complexity of the cooperative adjustment process of urban rail trains and the time-varying characteristics of the train operation environment. Combined with practical engineering, future research will focus on the following areas:  
* Multiple trains adaptive cooperative anti-disturbance control with position output constraints under model uncertainty constraints and longer lasting external multi-source disturbance. The dynamic behavior of multiple trains is related to many factors, excluding their own traction and braking force, but also by air resistance, tunnel resistance, ramp resistance, route condition changes, and the running state of the preceding trains and other random interference factors. So, it is very difficult to establish an accurate model that can portray so many factors, and at the same time, the model established by considering too many factors is too complicated. Therefore, while ensuring the simplicity of the control algorithm, the design considering the model uncertainties and longer lasting disturbance is the key to further improving the engineering practicability. * Research on active fault-tolerant control of the running state adjustment process of urban rail multiple trains. The drift of train sensor parameters, the delay of multiple trains information interaction data transmission, and packet loss are unavoidable. Active fault-tolerant control that takes into account train sensor accuracy and communication channel capacity limitations will help to improve the reliability and applicability of multiple trains cooperative control.