## 1 Introduction
Despite the presence of actuator faults, the fault-tolerant control schemes mentioned above achieve good tracking performance. However, it is worth noting that actuator output saturation, which means that the control input is subject to a certain restriction, has not been concerned in the literature mentioned above. In fact, actuator output saturation is also an extremely crucial factor in practical systems [15]. Controllers designed without considering actuator saturation would suffer from performance degradation or even instability in the presence of actuator saturation [16; 17; 18]. Obviously, actuator faults and actuator output saturation should be considered simultaneously to obtain satisfactory tracking performance for HSTs. A series of control strategies have been proposed to deal with actuator faults and actuator saturation simultaneously [19; 20; 21]. However, only a handful of literature is exclusively for HSTs [22]. In [22], a neural adaptive control scheme based on a novel sliding mode surface was investigated for HSTs subject to unknown basic resistance, additional disturbance, actuator faults and actuator saturation. In the paper, the additional disturbance was approximated by RBF NN, so that the control performance depends, to some extent, upon the number of neurons and the NN parameters including the width, the centers (Gaussian NN) and so on. However, there lacks a general guideline for the choices of these parameters. Besides, the adoption of RBF NN would increase computational burden of the fault-tolerant tracking controller for HSTs. Moreover, parametric uncertainties were not concerned, which would influence control effect in practical train operation. The uncertainties of parameters, additional disturbance, actuator faults, and actuator saturation have great impacts on the stability and control performance of the control system. Therefore, how to design a robust controller for HSTs considering these factors simultaneously has become an urgent need. Motivated by the above analysis and inspired especially by the work of [PERSON] et al. [22], an adaptive passive fault-tolerant tracking control strategy based on a variable-gain PID-type sliding mode surface is presented for HSTs in which parametric uncertainties, additional disturbance, unknown actuator faults, and actuator output saturation are taken into account simultaneously. The adopted variable-gain PID-type sliding mode surface is featured with variable gains and can offer fast transient response, low steady-state error, and strong robustness [23]. An adaptive adjustment technique is employed to estimate the nominal model parameters, upper bounds of the lumped uncertainty, and gains of the PID-type sliding mode surface, respectively. An auxiliary signal is introduced to deal with actuator saturation. The proposed strategy is fully model-independent and does not require the information of actuator faults. As a result, simple structure and inexpensive computation are achieved, which is exactly what is expected in practical application. Based on Lyapunov theory and simulation results, it is analyzed and demonstrated that the proposed controller can track the desired position and velocity trajectories accurately, and has strong robustness to the lumped uncertainty and the actuator faults. The rest of this paper is organized as follows. Section 2 provides the train dynamical model and formulates the problem statement. Section 3 derives the adaptive passive fault-tolerant tracking control strategy for HSTs based on variable-gain PID-type sliding mode surface. Section 4 presents the simulation results and verifies the effectiveness of the control strategy. Finally, some concluding remarks are given in Section 5.