Hierarchical optimal control framework to automatic train regulation combined with energy-efficient speed trajectory calculation in metro lines

In high-density metro lines, frequent disturbances could lead to a domino effect of train delays if no adjustment strategy is imposed timely. In this paper, to enhance train timetable adherence and reduce energy consumption, we provide a hierarchical optimal control framework for the automatic train regulation problem with energy-efficient speed trajectory based on the model predictive control method. Specifically, by considering the dynamic passenger flows, the non-linear train regulation model is proposed at the higher level to enhance timetable adherence, while at the lower level the energy-efficient speed trajectories of the trains are generated on-line in a distributed manner. The interaction of real-time information exists between the higher level and the lower level, i.e., the upper model provides the train running time and the numbers of onboard passengers to the lower model, while the lower model feedbacks the updated train information (e.g., the actual arrival time) to the upper model, which provides the potential for the proposed framework to respond to disturbances at the operational stage. Moreover, a customized model predictive control method combined with Radau pseudospectral method (RPM) is designed to generate the energy-efficient train speed trajectory at the lower level in response to uncertain operational conditions. Numerical cases based on the Beijing Metro Yizhuang line demonstrate the effectiveness and robustness of our proposed hierarchical optimal control framework to deal with uncertain disturbances.