On an optimal control problem of train operation

By E. Khmelnitsky. IEEE Transactions on Automatic Control, 2000

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A Subway Train Timetable Optimization Approach Based on Energy-Efficient Operation Strategy (2012, background): “Example 1: Taking the interstation between Jiugong and Yizhuangqiao for example, there are three sections with speed limits:13 m/s for section {0 m ≤ s ≤ 180 m}; 20 m/s for section {180 m ≤ s ≤ 2074 m}; and 13 m/s for section {2074 m ≤ s ≤ 2265 m}.”
An Energy-Efficient Train Operation Approach by Integrating the Metro Timetabling and Eco-Driving (2020, unknown): “Khmelnitsky [6] and Liu et al.”
Single-Train Trajectory Optimization (2013, methodology): “Because the methods using optimal control theories can be integrated with the fast response characteristics, they can be applied to develop online optimum control systems [8], [10].”
Optimal trajectory planning for trains – A pseudospectral method and a mixed integer linear programming approach (2013, background): “Khmelnitsky (2000) states that this assumption is not restrictive in practice for two reasons.”
Optimal trajectory planning for trains under fixed and moving signaling systems using mixed integer linear programming (2014, background): “…velocity,6 which depends on the train characteristics and line conditions, and as such it is usually a piece-7 wise constant function of the coordinate s (Khmelnitsky, 2000; Liu & Golovicher, 2003); sstart,8 Ẽ(sstart), and t(sstart) are the position, the kinetic energy per mass, and the…”