## 1 Introduction
[15; 16] do not consider the problem of fault-tolerant control of traction or braking mechanism. In recent research results, ref. [17] made up for the fault tolerance problem that was not considered in [15; 16] and designed a model-free adaptive fault-tolerant control (MFA-FTC). The controller only uses the input and output data generated during train operation and does not need to establish the train dynamics model, which has become a current research hot spot. What needs our attention is in model-free adaptive control, the dynamic linear data model only establishes the connection between the input and output data of the system and does not have a clear physical meaning. It is impossible to predict and analyze the dynamic behavior of the train based on the model. For the train operation environment with large external interference, the current model-free adaptive control method is difficult to guarantee a consistent train operation control performance index for a long time. Based on the above problems, this paper considers the state tracking problem with actuator failure, delay, and control input limitation and proposes a radial basis function neural network adaptive terminal sliding mode fault tolerant control (ATSM-FTC-RBFNN) method to realize the accurate tracking control of urban rail train operation curve. Adaptive terminal sliding mode control is widely used in various fields because of its complete adaptability to the intrinsic parameter disturbances and external disturbances of the system and its convergence to the equilibrium point in finite time [18; 19]. Literature [20; 21; 22; 23] shows that RBFNN has strong real-time performance, nonlinear mapping ability, and strong adaptive ability and can approximate smooth nonlinear functions with any precision. Therefore, this paper introduces the additional resistance caused by the route section into an adaptive sliding mode controller in the form of disturbance by using RBFNN to enhance the anti-interference ability of the system to deal with the additional interference caused by the route slope and route radius. The following summarizes the main contributions of this paper. * An adaptive terminal sliding mode fault-tolerant algorithm based on RBFNN is proposed. The algorithm is based on ATSMC, FTC, and RBFNN. The initial trackingand approximation errors are explicitly considered, and the error boundary of system control parameters is given. At the same time, the boundary value can be adjusted to any small value by selecting appropriate parameters. * The RBFNN is introduced into the adaptive sliding mode controller in the form of disturbance, which can effectively reduce the acquisition of route information, such as route slope and route radius, and restrain the disturbance caused by the train in the tunnel. * In order to improve the engineering practicability of the ATO controller, uncertainty, external interference, control input saturation, sensor time delay, and traction or braking fault are considered in the design of the ATO controller to match the actual train operation conditions. * In order to further verify the effectiveness of the designed controller, the complex route conditions are selected for simulation experiments. MATLAB simulation results show that the proposed ATO control algorithm has excellent anti-interference ability, can effectively reduce the system switching gain, smooth the control input, and make the train zero error or very small error to track the desired curve in a shorter time. The paper is structured as follows. Section 2 introduces the function and working principle of ATO. Section 3 illustrates the nonlinear dynamic model of train operation. Section 4 proposes the RBFNN adaptive terminal sliding mode fault-tolerant controller. Section 5 provides the MATLAB simulation results to illustrate the proposed method. Section 6 discusses the results. Section 7 concludes the article.