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Virtual Coupling (VC) is regarded as a breakthrough to the traditional train operation and control for improving the capability and flexibility in railways. It brings benefits as trains under VC are allowed to operate much closer to one another, forming a virtually coupled train set (VCTS). However, the safe and stable spacing between trains in the VCTS is a problem since there are no rigid couplers to connect them into a fixed formation, especially in high-speed scenarios. Due to the close spacing, the interference between trains becomes non-negligible as various maneuvers of the preceding train can significantly affect driving behaviors of the following train; this results in fluctuating spacing and therefore an unstable VCTS. Aiming at minimizing the interference and maintaining constantly safe spacing between trains in the VCTS, this paper presents a distributed model predictive control (DMPC) approach for solving the high-speed VCTS control problem. Particularly, the proposed control method focuses on the feasibility and stability of this problem, with considerations of the coupled constraint of safety braking distance and the individual constraints of speed limit variations and restricted traction/braking performance. To guarantee feasibility and stability, the terminal controller and invariant set of the DMPC are designed. For rigor, sufficient conditions of feasibility and stability are mathematically proved and derived. Based on the data of the Beijing-Shanghai high-speed railway line, numerical experiments are conducted to verify the correctness of derived sufficient conditions and the effectiveness of the proposed control method under interference and disturbances. [ABSTRACT FROM AUTHOR]

Operation optimization for modern subway trains usually requires the speed curve optimization and speed curve tracking simultaneously. For the speed curve optimization, a multi-objective seeking issue should be addressed by considering the requirements of energy saving, punctuality, accurate parking, and comfortableness at the same time. But most traditional searching methods lack in efficiency or tend to fall into the local optimum. For the speed curve tracking, the widely applied proportional integral differential (PID) and fuzzy controllers rely on complicated parameter tuning, whereas robust adaptive methods can hardly ensure the finite-time convergence strictly, and thus are not suitable for applications in fixed time intervals of trains. To address the above-mentioned two problems, this paper presents a novel approach for speed curve seeking and tracking control. First, we present the random reinforcement genetic algorithm (GA) algorithm to avoid the local optimum efficiently. Then, a sliding mode controller is developed for speed curve tracking with bounded disturbance. The Lyapunov theory is adopted to prove that the system can be stabilized in the finite time. Finally, using the real datasets of Yizhuang Line in Beijing Subway, the proposed approach is validated, demonstrating its effectiveness and superiorities for the operation optimization. [ABSTRACT FROM AUTHOR]