## 1 Introduction  
Along with the increase of departure density of high-speed trains (HSTs) and higher requirements for punctuality, security and reliability, how to get accurate position and velocity tracking to desired curves under different environments is becoming increasingly important. Consequently, considerable train tracking control schemes have been employed [1; 2; 3; 4; 5]. It is noted that some of the existing tracking control methods are model-dependent, which means that either entire or partial model parameters such as train mass, resistance coefficients, or additional disturbance of HSTs, are required as a priori. However, the model parameters and additional disturbance of HSTs are uncertain and variable due to many factors such as changes of passengers and loads, line conditions, weather, train speed, etc. [6; 7]. Thus, it is difficult to get precise knowledge of a train model in practice. In addition, parametric uncertainties are neglected in the control schemes mentioned above. Ignoring parametric uncertainties would give rise to certain control deviation, which makes it difficult to maintain good control performance in practical train tracking operation. Therefore, the discussion mentioned above leads to a motivation to design a tracking control strategy for HSTs without the requirementsof precise model parameters, whereas with strong robustness against additional disturbance and parametric uncertainties. To solve the problems stated above, in [8], a model-independent position and velocity tracking control strategy based on robust adaptive nonsingular terminal sliding mode was proposed for HSTs with model parametric uncertainties and additional disturbance. The proposed controller achieves good tracking performance and strong robustness. Despite the efforts above, the inescapable occurrence of actuator faults during the long-term and long-distance train operation is not considered. Actuator faults may deteriorate train performance severely and even threaten the safety of passengers' lives and property. However, due to the uncertainties of actuator faults in amplitudes and instants, it is challenging to compensate for the failures and maintain good tracking performance. Fault-tolerant control is a good solution to guarantee safe and reliable operation of HSTs subject to actuator faults. There are two kinds of fault-tolerant control approaches: active fault-tolerant control and passive fault-tolerant control. Performance of the former depends heavily on the accuracy and timelessness of fault detection and diagnosis module, while the latter does not require fault information feedback [9]. As a result, passive fault-tolerant control can compensate for fault effects much faster. Thus, many efforts on passive fault-tolerant tracking control for HSTs have been addressed [10; 11; 12; 13; 14]. In [10], a fault-tolerant controller using a so-called virtual-parameter-based backstepping adaptive control method was designed. It is fully parameter independent and can guarantee closed-loop tracking stability of the train system. In [11], in the face of actuator faults with unknown amplitudes and occurrence time, an adaptive fault-tolerant control scheme based on radial basis function (RBF) neural networks (NN) was adopted and asymptotical position and speed tracking was achieved. In [12], two novel adaptive fuzzy fault-tolerant control schemes with proportion-integral (PI)-based sliding mode were investigated to deal with the actuator failures of HSTs with uncertain parameters, unknown non-linear dynamics, and external disturbances. In [13], a neuroadaptive proportion-integral-derivative (PID)-like controller for HSTs was developed, which is independent of train model and insensitive to system uncertainties, additional disturbance, as well as actuator faults. In [14], a failure compensation controller was proposed for HSTs in the presence of actuator faults, time-varying system parameters, and disturbances.