# Research on Active Anti-Slip Control of High-Speed Trains Based on High-Order Sliding Mode
## 1 Introduction  
With the global expansion of high-speed rail, high-speed trains have become essential to modern transportation due to their capacity, speed, and safety. However, they often encounter complex track conditions, particularly variations in wheel-rail adhesion. Low-adhesion track surfaces, caused by factors such as rain, snow, or oil, can lead to wheel slip, compromising operational efficiency and safety. To address the challenge of ensuring stable train operation under low-adhesion conditions, numerous researchers have conducted in-depth studies. However, many existing studies assume that traction and braking forces can be directly controlled, overlooking the complex variations in wheel-rail adhesion that occur in practical operations [1]. A predictive train model controller has been developed that accounts for traction and braking forces, physical limitations, and passenger comfort constraints. Although this controller improves energy efficiency by adjusting the traction force curve in real time, it does not fully account for varying adhesion conditions, which are essential for maintaining stability under dynamic track conditions [1]. The reliance on energy efficiency for real-time adjustments is helpful but does not consider the critical impact of wheel-rail slip under low-adhesionconditions [2]. Similarly, a robust predictive controller and an iterative learning controller within a multi-agent framework have been introduced. While both approaches enhance control system adaptability, they still oversimplify traction control by assuming idealized conditions that ignore the impact of wheel-rail adhesion variations, which can lead to suboptimal performance in real-world applications [2; 3]. Train operations are often subject to disturbances and faults, making fault tolerance a critical aspect of control design. A composite adaptive anti-disturbance fault-tolerant controller has been proposed to address this issue. Although this controller improves system robustness by tracking the given speed profile, it overlooks the role of adhesion in fault tolerance. Disturbances that affect wheel-rail contact, such as low-adhesion conditions, are not adequately considered in this approach, and as a result, its performance could degrade under these challenging conditions [4]. Sliding mode control has also been widely recognized for its effectiveness in handling disturbances and faults. A sliding mode train operation controller based on a dynamic model with actuator fault uncertainty has been designed, while another improvement to the sliding mode controller incorporates non-singular terminal sliding mode theory to address uncertainties in system parameters and external disturbances. These approaches improve robustness but still fail to incorporate the dynamic nature of adhesion, which plays a crucial role in system performance under varying track conditions [5; 6]. While some researchers have made strides in incorporating adhesion characteristics into train control, such as a learning-based controller and a sliding mode tracking controller using linear adhesion properties, these models oversimplify the complex behavior of adhesion. They often assume linearity or fail to capture the full range of wheel-rail interactions, particularly under low-adhesion conditions. These simplifications neglect the nonlinear and time-varying nature of adhesion, which significantly influences train stability and control [7; 8]. Most existing studies also fail to address the critical issue of anti-slip control for train wheels under low-adhesion conditions, where the friction between the wheel and rail decreases drastically, leading to wheel slip. This unresolved problem remains a challenge for effective train control and highlights the need for further research into accurate adhesion models and control strategies that can adapt to the dynamic and nonlinear variations in adhesion during real-world operations [9; 10].