Dynamic speed trajectory generation for virtual coupling train operations with multi-state transitions in rail transit system

The development of train control technology has facilitated the investigation into more flexible organization modes in railway industry. This paper studies the speed trajectory generation problem with the coupling and decoupling process in rail transit systems under the model predictive control framework. Considering the constraints of train dynamic operations, boundary conditions, and train safety distance, a nonlinear optimization model with disjunctive constraints is formulated to capture the complex logic relationship existing in the process containing multi-state transitions. To obtain an effective speed trajectory in real-time, a logic-based algorithm is designed, providing an efficient way to deal with the model with disjunctive constraints. An outer approximation cut is introduced to the mixed-integer linear programming master problem, which is solved alternatively with the nonlinear programming sub-problem. Numerical simulations are conducted to validate the effectiveness of the proposed model and method. Computational results demonstrate that the proposed speed trajectory generation method effectively yields smooth speed trajectories, leading to a better coupling and decoupling performance.