Abstract With the rapid development of autonomous vehicles, heavy-haul freight trains (HhFT), with their capability of transporting large volumes of cargo over long distances, are emerging as promising subjects for research in automatic control. One of the main challenges in operating HhFT lies in ensuring accurate trajectory tracking performance under the influence of adverse factors such as external disturbances, model uncertainties, and actuator-related issues, including actuator faults and input time delays. If not effectively addressed, these factors can significantly degrade the control performance of the system. This paper presents a robust trajectory tracking control system with prescribed performance for HhFTs using multiple electric locomotives. In this framework, a prescribed performance function (PPF) is designed to ensure that the position tracking errors of the locomotives remain within a predefined bound. Simultaneously, an extended state observer (ESO) is employed to estimate the states and the lumped disturbances representing the adverse effects. Based on the outputs of the PPF and the ESO, a robust sliding mode controller is designed. The stability of the closed-loop system is proven through Lyapunov stability theory, showing that all system states converge to a neighborhood of the origin in finite time. Computer simulation results clearly demonstrate the superior control performance of the proposed system compared to previously introduced methods.
Nguyen et al. (2026) studied this question.