More and more people in big cities choose urban rail transit as the main means of public transportation. With the increasing unbalanced passenger flow in time and space, the traditional operation mode with fixed train formation (or composition) is difficult to satisfy the varying passenger demands. This paper distinguishes different train formations in urban rail transit, and specifies the definition and the operation process for flexible composition of trains. An integrated train scheduling problem with flexible train composition is proposed, where the key constraints for practical train operation and the utilization of rolling stocks are considered. These constraints involve turnaround constraints, flexible train formation constraints, headway constraints and passenger flow constraints. The resulting problem is a mixed integer nonlinear programming problem, which can be transformed into a mixed integer linear programming problem and then be solved using existing optimization solvers, e.g., CPLEX. Based on the practical infrastructure and passenger demand data of the Beijing Daxing International Airport Express, a set of case studies is carried out to demonstrate the effectiveness of the presented model and solution approach. The computational results show that the train schedule with flexible train compositions can largely reduce the number of waiting passenger when compared with the train schedules with fixed train compositions and with multiple train compositions.@en

In practice, the operation of high-speed trains is often affected by adverse weather conditions or equipment failures, which result in delays and even cancellations of train services. In this article, a novel two-layer hierarchical model predictive control (MPC) model is proposed for on-line high-speed railway delay management and train control for minimizing train delays and cancellations. The upper layer manages the global objectives of the train operation, that is, minimizing the total train delays and providing guidance for the speed control in the lower layer. The objectives of the lower layer are to satisfy the running time requirements given by the upper layer and to save energy at the same time. The optimization problems in both levels of the hierarchical MPC framework are formulated as small-scale mixed integer linear programming problems, which can be solved efficiently by existing solvers. Particularly, the train control problem is solved in a distributed way for each train. Simulation analysis based on the real-life data of the Beijing-Shanghai high-speed railway shows that the proposed hierarchical MPC framework can meet the real-time requirements and reduce train delays effectively when compared with widely accepted strategies, for example, first-scheduled-first-serve and first-come-first-serve. Moreover, the proposed hierarchical MPC framework also provides good robustness performance for different disturbance scenarios.

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The identification of affinely parameterized state–space system models is quite popular to model practical physical systems or networked systems, and the traditional identification methods require the measurements of both the input and output data. However, in the presence of partial unknown input, the corresponding system identification problem turns out to be challenging and sometimes unidentifiable. This paper provides the identifiability conditions in terms of the structural properties of the state–space model and presents an identification method which successively estimates the system states and the affinely parameterized system matrices. The estimation of the system matrices boils down to solving a bilinear optimization problem, which is reformulated as a difference-of-convex (DC) optimization problem and handled by the sequential convex programming method. The effectiveness of the proposed identification method is demonstrated numerically by comparing with the Gauss–Newton method and the sequential quadratic programming method.

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