Deep Koopman Operator Approach for Metro Train Dynamics Modeling and Speed Tracking Control

Traditional physics-based train models often oversimplify system dynamics, making them inadequate for modeling complex and nonlinear behaviors in practical scenarios, while purely data-driven models often lack physical interpretability. To address these limitations, this paper proposes a novel metro train dynamics modeling and control framework that integrates a Deep Koopman operator(DKO) with Model Predictive Control (MPC). A deep neural network (DNN) is utilized as the lifting function of Koopman operator, which eliminates the dependence on manually selected lifting functions and significantly enhances the model’s representational capacity. Furthermore, a Deep Learning-Enhanced Extended Dynamic Mode Decomposition (DLEDMD) method is employed for dimensionality reduction, enabling an explicit linear representation of the metro train. This linear structure facilitates the direct application of MPC for real-time and optimal train speed tracking. Experimental results demonstrate that the proposed approach achieves superior tracking performance compared to the actual onboard controller.