2016
DOI: 10.1016/j.trb.2016.08.002
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A multiphase optimal control method for multi-train control and scheduling on railway lines

Abstract: We consider a combined train control and scheduling problem involving multiple trains in a railway line with a predetermined departure/arrival sequence of the trains at stations and meeting points along the line. The problem is formulated as a multiphase optimal control problem while incorporating complex train running conditions (including undulating track, variable speed restrictions, running resistances, speed-dependent maximum tractive/braking forces) and practical train operation constraints on departure/… Show more

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Cited by 89 publications
(48 citation statements)
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“…The model complex M evolves and generalizes the dynamic models of scheduling theory [2][3][4]6,15]. The main distinctive feature (as apposed to [3]) of the complex is that nonlinear technological constraints are actualized in the convex domain of allowable control inputs rather DOI: 10.1051/ , 02012 (2017)than in differential equations.…”
Section: Resultsmentioning
confidence: 99%
“…The model complex M evolves and generalizes the dynamic models of scheduling theory [2][3][4]6,15]. The main distinctive feature (as apposed to [3]) of the complex is that nonlinear technological constraints are actualized in the convex domain of allowable control inputs rather DOI: 10.1051/ , 02012 (2017)than in differential equations.…”
Section: Resultsmentioning
confidence: 99%
“…Additionally, the requirements of network operation and various passengers demand should be satisfied [10][11][12][13][14][15]. Lastly, energy conservation and environmental protection should be considered [16][17][18][19][20][21]. Hence, TSSTT should not only meet the demands of compiling a working diagram at the network level under different passenger needs, but also should consider energy conservation and environmental protection while ensuring that the TSRT on the same railway section falls within the neighborhood of TSSTT.…”
Section: Introductionmentioning
confidence: 99%
“…TSRT based on traction calculation is determined by equations of motion combined with the relationship between train tractive and braking forces, the sum of mechanical and aerodynamic resistances, and force caused by the track gradient, which reflect the train's section traction, idling, and brake operation process [16][17][18][19]. Hence, noise factors such as weather and power supply [9] on the railway line are considered less in the calculation process.…”
Section: Introductionmentioning
confidence: 99%
“…Chevrier et al [1], Shoichiro and Koseki [2], Yang et al [3,4], Wang and Goverde [5], Ning et al [6], Zhang et al [7] and Yang et al [8] optimized the train timetable by adjusting the train running path, the arrival and departure time or the passing time of the train, and realized energy-saving operation. Albrecht et al [9][10][11], Scheepmaker and Goverde [12], Yan et al [13], Ye and Liu [14], Luan et al [15], Yang et al [16], Fernández-Rodríguez et al [17] under the constraints of train characteristics, ramps, curves and speed limits, achieved optimal operating conditions and reduced energy consumption by adjusting the acceleration, cruising, coasting and braking phase.…”
Section: Introductionmentioning
confidence: 99%
“…However, considering energy-saving issues from a single view of train timetables or train control methods, it may be di cult to nd a suitable energysaving strategy. erefore, the energy-saving schemes that combine these two angles are gradually becoming research focus Ye and Liu [14] established the multiphase optimal control problem to make the train's optimal strategy change with line conditions, and got the optimal train arrival and departure time under the condition of ensuring the safety interval. Ning et al [6] optimized the distribution of running time on the section and appropriately adopted a coasting state to reduce the energy consumption of the train during the speci ed total running time.…”
Section: Introductionmentioning
confidence: 99%