Physics-informed deep learning for virtual rail train trajectory following control

Trajectory-following control is a crucial challenge for virtual rail trains (VRTs), directly impacting tracking accuracy, path width requirements, and operational safety. Traditional model-based control methods, struggle with nonlinear dynamics and require highly accurate system models, while purely data-driven deep learning methods lack physical interpretability and robustness. To address these challenges, this paper proposes a novel Physics-Informed Deep Learning Control Strategy that integrates Lagrangian dynamics equations into a deep neural network, forming a Deep Lagrangian Neural Network (DLNN). This approach ensures that the learned control model retains essential physical properties while capturing complex vehicle dynamics. The DLNN serves as an inverse model within the control framework, mapping desired trajectories to control inputs. Experimental results on circular, lane-change, and obstacle-avoidance maneuvers demonstrate that the DLNN model significantly reduces lateral deviation and yaw rate errors compared to traditional Multi-Layer Perceptron (MLP)-based models. The DLNN exhibits strong generalization capability across different trajectory geometries and benefits from online learning, allowing continuous adaptation to new driving conditions. These findings highlight the potential of physics-informed deep learning in intelligent rail transit systems, providing a more accurate, interpretable, and robust control framework for virtual rail train trajectory following.