Abstract
When we formulate the optimal train control model for optimizing the operation strategy, it is necessary to consider the uncertain disturbances arising from the whether, route and locomotive rolling conditions. Stochastic energy-efficient operation has proved to be an efficient approach to reduce the effect of uncertainty by estimating the resistance coefficients as random variables. The purpose of this paper is to prove the existence of an optimal operation strategy. First, we prove the existence of a feasible operation strategy satisfying the nonnegativity, boundary conditions, trip distance and the motion equation. Furthermore, we prove the Lipschitz continuity for the stochastic objective function. Finally, we prove the existence theorem for an optimal operation strategy.
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Chang CS, Sim SS (1997) Optimising train movements through coast control using genetic algorithms. IEE Proc Electr Power Appl 144(1):65–73
Cheng J, Howlett PG (1993) A note on the calculation of optimal strategies for the minimization of fuel consumption in the control of trains. IEEE Trans Autom Control 38(11):1730–1734
Howlett PG (1988) Existence of an optimal strategy for the control of a train. School of Mathematics report 3, University of South Australia
Howlett PG (1990) An optimal strategy for the control of a train. ANZIAM J 31:454–471
Howlett PG, Pudney PJ (1995) Energy-efficient train control. Advances in industrial control. Springer, London
Howlett PG, Pudney PJ, Vu X (2009) Local energy minimization in optimal train control. Automatica 45:2692–2698
Ke BR, Chen N (2005) Signalling blocklayout and strategy of train operation for saving energy in mass rapid transit systems. IEE Proc Electr Power Appl 152(2):129–140
Ke BR, Chen MC, Lin CL (2009) Block-layout design using max–min ant system for saving energy on mass rapid transit systems. IEEE Trans Intell Transp Syst 10(2):226–235
Khmelnitsky E (2000) On an optimal control problem of train operation. IEEE Trans Autom Control 45(7):1257–1266
Kim K, Chien S (2010) Simulation-based analysis of train controls under various track alignment. J Transp Eng 136(11):937–948
Kim K, Chien S (2011) Optimal train operation for minimum energy consumption considering track alignment, speed limit, and schedule adherence. J Transp Eng 137(9):665–674
Kokotović P, Singh G (1972) Minimum-energy control of a traction motor. IEEE Trans Autom Control 17(1):92–95
Lee DH, Milroy IP, Tyler K (1982) Application of Pontryagin’s maximum principle to the semi-automatic control of rail vehicles. In: Proceedings of the second conference on control engineering, Newcastle, Institution of Engineers Australia, pp 233–236
Li X, Gao ZY, Tang T, Su S (2011) Train energy-efficient operation with stochastic resistance coefficients. Technical report
Liu R, Golovitcher I (2003) Energy-efficient operation of rail vehicles. Transp Res Part A Policy Pract 37:917–932
Milroy IP (1980) Aspects of automatic train control, Ph.D. thesis. Loughborough University
Miyatake M, Matsuda K (2009) Energy saving speed and charge/discharge control of a railway vehicle with on-board energy storage by means of an optimization model. IEEJ Transactions on Electr Electron Eng 4(6):771–778
Miyatake M, Ko H (2010) Optimization of train speed profile for minimum energy consumption. IEEJ Trans Electr Electron Eng 5(3):263–269
Morten WJ, Spencer CS (1997) Estimating emissions from railway traffic. Report for the project MEET: methodologies for estimating air pollutant emissions from transport
Wong KK, Ho TK (2004) Dynamic coast control of train movement with genetic algorithm. Int J Syst Sci 35:835–846
Yang L, Li K, Gao Z (2009) Train timetable problem on a single-line railway with fuzzy passenger demand. IEEE Trans Fuzzy Syst 17(3):617–629
Yang L, Gao Z, Li K (2011) Railway freight transportation planning with mixed uncertainty of randomness and fuzziness. Appl Soft Comput 11:778–792
Yang L, Gao Z, Li K, Li X (2012) Optimizing trains movement on a railway network. Omega Int J Manag Sci 40:619–633
Acknowledgments
This work was supported by the National Natural Science Foundation of China (No. 71101007), the National High Technology Research and Development Program of China (No. 2011AA110502), the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20110009120036), the State Key Laboratory of Rail Traffic Control and Safety (No. RCS2010ZT002), and the Fundamental Research Funds for the Central Universities (No. 2011JBZ014).
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Li, X., Gao, Z. & Sun, W. Existence of an optimal strategy for stochastic train energy-efficient operation problem. Soft Comput 17, 651–657 (2013). https://doi.org/10.1007/s00500-012-0938-x
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DOI: https://doi.org/10.1007/s00500-012-0938-x