Abstract
In this chapter, the optimal trajectory planning problem for multiple trains under fixed block signaling systems and moving block signaling systems is considered. Two solution approaches are proposed to solve this optimal control problem for multiple trains: the greedy approach and the simultaneous approach. The greedy approach optimizes the trajectories of trains sequentially, where first the trajectory of the leading train is optimized and then the trajectory of the following train is optimized based on the trajectory of the leading train. In the simultaneous approach, the trajectories of all the trains are optimized at the same time. In each approach, the trajectory planning problem is similar to the problem of Chap. 3, and therefore it can also be solved using the pseudospectral method and the mixed integer linear programming (MILP) approach. The performance of the proposed approaches is compared via a case study. This chapter is based on Wang et al. (Control Eng Pract 22:44–56, 2014) [1] and is supported by the results presented in Wang et al. (Proceedings of the 12th European control conference, Zürich, Switzerland, pp 4556–4561, 2013) [2]; Wang et al. (Proceedings of the 5th international seminar on railway operations modelling and analysis (RailCopenhagen), Copenhagen, Denmark, 2013) [3].
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Notes
- 1.
As stated in Chap. 2, there exist four MBS schemes: moving space blocking signaling, moving time block signaling, pure MBS, and relative MBS. In this book, we only consider the pure MBS system, so the MBS system later on refers to the pure MBS system.
- 2.
Note however that the MILP approaches and the pseudospectral methods can also be applied if more than 2 stations are considered.
- 3.
Tomlab website: http://tomopt.com.
References
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Wang, Y., Ning, B., van den Boom, T., De Schutter, B. (2016). Optimal Trajectory Planning for Multiple Trains. In: Optimal Trajectory Planning and Train Scheduling for Urban Rail Transit Systems. Advances in Industrial Control. Springer, Cham. https://doi.org/10.1007/978-3-319-30889-0_4
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DOI: https://doi.org/10.1007/978-3-319-30889-0_4
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