Evolution of Control Capability in Virtually Coupled Train Convoys Using State Transition-Based Chain MPC as a Benchmark

Virtually coupled train convoy control represents a cutting-edge area of research in railway transportation. To address challenges in achieving consistent train behavior while balancing safety, efficiency, and smoothness in convoy control, a dynamic safety distance model, passing through the coordinate origin, is developed to fully utilize station capacity, with the safe and efficient steady-following state as the target of the state transition process. To achieve safe, efficient, and smooth train following, a state transition-based chain model predictive control (MPC) method is proposed. This approach facilitates the establishment, maintenance, and recovery of a safe and efficient steady-following state, or the initiation of a new one, thereby promoting cooperation and consistency among trains within the virtually coupled train convoy. Subsequently, the optimal trainfollowing behavior derived from the state transition-based chain MPC, tested under diverse scenarios in complex transportation environments, serve as a benchmark for evolving train control capabilities. To tackle issues such as gradient vanishing and explosion, a zero-centered symmetric, rotated-piecewise tanh activation function is introduced. This function supports the development of a deep neural network (DNN) designed to overcome the limitations of the state transition-based chain MPC algorithm, particularly in achieving both real-time performance and global optimization. Finally, an evolutionary algorithm based on DNN iteration is proposed to enhance train intelligence. Simulations demonstrate the feasibility and effectiveness of the proposed approach in improving safety, efficiency, and smoothness, as well as achieving consistency in distributed train behaviors within the convoy by attaining the safe and efficient steady-following state.