Research on predictive control of train speed based on BFGS method

Train speed control is a crucial and fundamental problem in the development of rail transportation. Designing dynamic models and controllers for real-world train speed control applications is highly challenging. Traditional feedback-based model-free control strategies suffer from slow convergence, high parameter requirements, sensitivity to environmental changes, and difficulty in designing controllers from the optimization perspective, thus making it challenging to handle constraints in complex systems. On the other hand, traditional single-mass-point dynamic models of trains are inadequate in dealing with the nonlinear characteristics that arise from high-speed train operations. To address these challenges, a multi-mass-point model of the train was first constructed, which took into account the mechanical analysis of each carriage and the safe distance between them. In the proposed model, the relative position and relative velocity were considered as the variable states. Second, a model predictive control strategy was exploited to consider the nonlinear cost function of train speed control, handle complex constraints in train operations, and predict the future dynamic behavior of the control system. Third, for the nonlinear optimization problem in predictive train control with complex dynamic constraints, logarithmic barrier functions were used to handle inequality constraints. A BFGS-based predictive train speed algorithm with guaranteed stable convergence was developed from the perspective of quasi-Newton methods to achieve precise tracking control of train speed. Finally, a comparison experiment with other advanced control methods was conducted to verify the superior performance of the proposed BFGS-based predictive train speed algorithm by taking the train operation data between stations in China as an example. The experimental results show that the proposed BFGS-based predictive train speed algorithm designed in this paper can effectively reduce the train speed tracking error and displacement error, improve the tracking accuracy of train speed, and is conducive to ensuring the safety, punctuality, high efficiency, and stability of trains. The findings could provide a new idea for the development of rail transit train speed control technology. © 2024, Central South University Press. All rights reserved.