State-Space Modeling and Feedback Control for Real-Time Automatic Train Timetable Rescheduling of Intercity HSRs

In intercity high-speed railways (HSR) with high speeds and dense traffic, fast decision-making in timetable rescheduling is critical to minimize delays and maintain regular services during disruptions. Different from traditional mathematical programming methods, which are often too computation-intensive for real-time implementation, this paper develops a state-space dynamic model of train traffic with the extension to accommodate multiple trains in the sections between stations. Variations of the state space model are established for scenarios of mild delays and severe delays, respectively. Two automatic rescheduling state feedback controllers are designed to achieve two objectives, to restore the nominal timetable in case of mild delays and to retain regular departure intervals in case of severe delays, respectively. Stability analysis theoretically proves the stability and convergence of the proposed feedback controller and real-time rescheduling algorithm. The proposed rescheduling method indeed is a real-time state feedback controller, and the simulation results of the Beijing-Tianjin intercity HSR show that the proposed method features negligible computation times in the order of microseconds, in contrast to the 56s and 65s required by conventional Mixed-Integer Programming (MIP) for nominal timetable recovery and regular departure interval problems, respectively. The proposed state-space feedback control rescheduling method is quasi-optimal compared to MIP with the added advantage of greater computational efficiency and fast decision-making.