A Distributed Model Predictive Control Approach for Virtually Coupled Train Set with Adaptive Mechanism and Particle Swarm Optimization

Virtual coupling (VC) technology, which determines the safe interval between trains based on relative braking distance, offers a promising solution by enabling tighter yet safe train-following intervals through advanced communication and control strategies. This paper focuses on addressing the virtually coupled train set (VCTS) control problem within the framework of distributed model predictive control (DMPC), in which train dynamics model incorporates uncertainties in basic resistance and control inputs, with an adaptive mechanism (ADM) designed to limit errors caused by external disturbances. A multi-objective cost function is established, considering position error, speed error, and ride comfort, while constraints such as actuator saturation, speed limits, and safe tracking distance are enforced. Particle swarm optimization (PSO) is employed to solve the non-convex optimization problem globally. Simulation experiments validate the effectiveness of the proposed method, demonstrating stable operation of VCTS under various initial conditions and the ability to handle uncertainties through the adaptive mechanism. The results show that the proposed DMPC approach significantly reduces tracking errors and improves ride comfort, highlighting its potential for enhancing railway capacity and operational efficiency.