Using a high-gain disturbance observer（HGDO）, a self-adaptive nonsingular terminal sliding mode control (ANTSMC) approach is devised to solve the issue of control performance degradation in magnetic levitation ball systems caused by modeling errors and unknown disturbances. First, a model of the maglev ball system is developed and the model is linearized at the equilibrium point. Then, to weaken the chattering of the sliding mode controller and guarantee the finite-time convergence of tracking errors, an adaptive nonsingular terminal sliding mode controller is designed. To estimate the lumped disturbance, a high-gain disturbance observer is employed. Theoretical convergence findings demonstrate that the suggested high-gain disturbance observer may rapidly converge to an adjustable neighborhood of real disturbance values. Adaptive nonsingular terminal sliding mode control law with disturbance compensation is designed based on the disturbance estimation, the system is proven globally uniformly and ultimately bounded under the control law. According to simulation and quantitative analysis, the system's robustness under the same control method is improved when the controller with a high-gain disturbance observer lowers the integral time squared error（ITSE）value by 75% and the integral time absolute error（ITAE） value by 60% for the total disturbance observation error when compared to the controller with a generalized proportional-integral observer.

The safety of operating formation trains is now subject to stricter standards due to the high speed and high density tracking control of trains. To meet the need for precision and adaptability during train operation, an adaptive model predictive control (MPC) technique based on an artificial potential field is created for virtual coupled (VC) systems. First, a VC train is used as the research object, and the MPC method is used to create a dynamic model based on the equilibrium state of the train, with control accuracy and smoothness as the optimization objectives. Next, a collision avoidance function based on an artificial potential field setting is added to the objective function, allowing for the realization of the formation’s collision avoidance control. In order to improve the real-time performance of the system and ensure accurate control of the train formation, it is also necessary to analyze the impact of various time domain parameters on the control accuracy and computational efficiency of the system, design the corresponding adaptation function, and base this on a genetic algorithm (GA) that can find the best combinations of time domain parameters under various working conditions. On the MATLAB platform, a 4-train tracking operation scenario is developed as a last step to test the effectiveness of the suggested approach. The study’s findings demonstrate that the artificial potential field-based model predictive controller has interval control accuracy that is 94.8% greater than that of the conventional model predictive controller, successfully preventing train collisions and ensuring the safety of train operation. Furthermore, the adaptive control law controller may adjust the system in real-time based on the train’s operational status, resulting in a 10% increase in computing efficiency and excellent control accuracy. The study’s findings support the viability of the suggested control approach, enhance the controller’s overall control performance, and serve as a guide for future improvements in formation control and ensuring safe train operation.