## 1 Introduction  
Urban rail transit's FAO (fully automatic operation system) is a direct control unit to ensure the safe operation of a train, and its advanced control algorithm is the core to ensure train control accuracy, comfort, and safe operation [1]. The use of an FAO controller with high control accuracy, less braking or traction switching times, and fast response speed is the key to ensure the safe and efficient operation of an urban rail train under a changeable operating environment and time-varying system status [2]. In the process of the development of the train FAO, FAO control algorithms have mainly included PID control [3], fuzzy control [4], neural network control [5], adaptive control [6], sliding mode control [7], predictive control [8], iterative learning [9], and the combination of various control methods [10]. The authors of [11] applied a train control algorithm based on fuzzy prediction to ensure the train's accurate tracking of the desired operation curve; however, the quadratic programming algorithm used in predictive control was time-consuming in the solution process, and the real-time performance was not easy to guarantee. The authors of [12] proposed an adaptive iterative learning control based on iterative variable parameters and measurement noise, which realized train operation control via the online modification of control parameters, but the real-time performance of continuous iteration was poor. The authors of [13] designed a sliding model using PID control for an automatic train operation system, which constrained the train operation to the sliding hyperplane so as to realize tracking and accurate parking of the desired operation curve, but the influence of unknown disturbances on the train operation control was not considered, and the control accuracy could not be guaranteed under complex road conditions. The authors of [14] proposed an accurate parking control algorithm of an urban rail transit train based on adaptive terminal sliding mode control, which can adaptively adjust the control input according to the model parameter changes caused by the uncertainty of train dynamic model parameters and unknown disturbance to ensure that the train can accurately track the desired parking curve. However, too many control parameters were designed, which affected the response speed and control accuracy of the system. The authors of [15] proposed an automatic train operation speed control method based on active disturbance rejection control (ADRC). The unknown part of the train dynamics model was taken as the extended state to design a second-order ADRC. Although it had the advantages of strong anti-interference and small tracking error, the algorithm only considered the influence of basic resistance on the train operation when the train was operating on straight routes, whereas it did not consider the additional resistance caused by route conditions such as route curve and slope. However, the FAO control and optimization were typical nonlinear problems. On the one hand, the train operation is affected by many complex factors such as route conditions, external environment, unknown disturbances, and train performance. The complex and changeable train operation environment and the inevitable existence of modeling errors lead to the uncertainty and time-varying characteristics of system parameters, which increases the difficulty of control design. On the other hand, the strict requirements of simplicity and real-time operation of the FAO control algorithm ensure the engineering practicability of the designed algorithm. Therefore, in order to ensure the control performance indices of high-precision control, smooth operation, and fast response of the FAO, the above aspects must be fully considered in the design of FAO controller, so that the designed FAO control algorithm can be applied in engineering [16].