Integrated train dwell time regulation and train speed profile generation for automatic train operations on high-density metro lines: A distributed optimal control method

The wide-spread application of automatic train operation (ATO) system on metro lines allows short service headways, high-density operations and high operation efficiency. This paper addresses real-time train control for ATO when faced with disturbances or disruptions in its operations. More specifically, the paper focuses on the design of integrated train dwell time regulation and speed profile generation in real-time and in response to dynamic changes in the operation environment. A nonlinear optimal control model is formulated in a rolling horizon scheme that incorporates three key operating elements: train timetable, passenger load and train speed profile. The objective is to simultaneously improve headway regularity and reduce the total energy consumptions. To satisfy the real-time control requirement for ATO system, a decomposition method based on the alternating direction method of multipliers (ADMM) is designed to divide the original optimization problem into many sub-problems, one for each train, which can then be computed in a distributed manner. Moreover, to address the non-convexity issue, a relax-round-polish process is developed to deal with the formulated nonlinear optimal control problem with convex objective over non-convex constraints in order to find the approximate solutions quickly for the embedded applications. The combined result is an ADMM-based heuristic algorithm. The effectiveness of the proposed model and solution algorithm is demonstrated using real-world data from the Changping Line of Beijing Metro. The results show that the proposed distributed and embedded optimization algorithm is able to significantly enhance the robustness and reliability of real-time train control in automated high-density metro lines.