IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i4p1035-d1072856.html
   My bibliography  Save this article

Optimal Control Problem for Minimization of Net Energy Consumption at Metro

Author

Listed:
  • Constantin Udriste

    (Department of Mathematics and Informatics, Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independentei 313, RO-060042 Bucharest, Romania
    Academy of Romanian Scientists, Ilfov 3, RO-050044 Bucharest, Romania
    These authors contributed equally to this work.)

  • Ionel Tevy

    (Department of Mathematics and Informatics, Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independentei 313, RO-060042 Bucharest, Romania
    These authors contributed equally to this work.)

  • Paun Antonescu

    (Department of Mechanisms and Robot Theory, University Politehnica of Bucharest, Splaiul Independentei 313, RO-060042 Bucharest, Romania
    These authors contributed equally to this work.)

Abstract

The optimal control currently decides the minimum energy consumption within the problems attached to subways. Among other things, we formulate and solve an optimal bi-control problem, the two controls being the acceleration and the feed-back of a Riemannian connection. The control space is a square, and the optimal controls are of the bang–bang type. The third component of the optimal solution is the maximum value function, as a solution of the Hamilton–Jacobi–Bellman PDE. The examples of energy optimal trajectories refer to the lines of the Bucharest subway.

Suggested Citation

  • Constantin Udriste & Ionel Tevy & Paun Antonescu, 2023. "Optimal Control Problem for Minimization of Net Energy Consumption at Metro," Mathematics, MDPI, vol. 11(4), pages 1-11, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:1035-:d:1072856
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/4/1035/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/4/1035/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Cacchiani, Valentina & Toth, Paolo, 2012. "Nominal and robust train timetabling problems," European Journal of Operational Research, Elsevier, vol. 219(3), pages 727-737.
    2. Goverde, Rob M.P. & Scheepmaker, Gerben M. & Wang, Pengling, 2021. "Pseudospectral optimal train control," European Journal of Operational Research, Elsevier, vol. 292(1), pages 353-375.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. M. Shakibayifar & A. Sheikholeslami & F. Corman & E. Hassannayebi, 2020. "An integrated rescheduling model for minimizing train delays in the case of line blockage," Operational Research, Springer, vol. 20(1), pages 59-87, March.
    2. Wang, Dian & D’Ariano, Andrea & Zhao, Jun & Zhong, Qingwei & Peng, Qiyuan, 2022. "Integrated rolling stock deadhead routing and timetabling in urban rail transit lines," European Journal of Operational Research, Elsevier, vol. 298(2), pages 526-559.
    3. de Lima, Vinícius L. & Alves, Cláudio & Clautiaux, François & Iori, Manuel & Valério de Carvalho, José M., 2022. "Arc flow formulations based on dynamic programming: Theoretical foundations and applications," European Journal of Operational Research, Elsevier, vol. 296(1), pages 3-21.
    4. Omar J. Ibarra-Rojas & Fernando López-Irarragorri & Yasmin A. Rios-Solis, 2016. "Multiperiod Bus Timetabling," Transportation Science, INFORMS, vol. 50(3), pages 805-822, August.
    5. Polinder, G.-J. & Cacchiani, V. & Schmidt, M.E. & Huisman, D., 2020. "An iterative heuristic for passenger-centric train timetabling with integrated adaption times," ERIM Report Series Research in Management ERS-2020-006-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    6. Schön, Cornelia & König, Eva, 2018. "A stochastic dynamic programming approach for delay management of a single train line," European Journal of Operational Research, Elsevier, vol. 271(2), pages 501-518.
    7. Krier, Betty & Liu, Chia-Mei & McNamara, Brian & Sharpe, Jerrod, 2014. "Individual freight effects, capacity utilization, and Amtrak service quality," Transportation Research Part A: Policy and Practice, Elsevier, vol. 64(C), pages 163-175.
    8. Ruf, Moritz & Cordeau, Jean-François, 2021. "Adaptive large neighborhood search for integrated planning in railroad classification yards," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 26-51.
    9. Polinder, G.-J. & Schmidt, M.E. & Huisman, D., 2020. "Timetabling for strategic passenger railway planning," ERIM Report Series Research in Management ERS-2020-001-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    10. Gábor Maróti, 2017. "A branch-and-bound approach for robust railway timetabling," Public Transport, Springer, vol. 9(1), pages 73-94, July.
    11. Hartleb, Johann & Schmidt, Marie, 2022. "Railway timetabling with integrated passenger distribution," European Journal of Operational Research, Elsevier, vol. 298(3), pages 953-966.
    12. Xiaoming Xu & Keping Li & Lixing Yang & Ziyou Gao, 2019. "An efficient train scheduling algorithm on a single-track railway system," Journal of Scheduling, Springer, vol. 22(1), pages 85-105, February.
    13. Hassini, Elkafi & Verma, Manish, 2016. "Disruption risk management in railroad networks: An optimization-based methodology and a case studyAuthor-Name: Azad, Nader," Transportation Research Part B: Methodological, Elsevier, vol. 85(C), pages 70-88.
    14. Andreas Bärmann & Alexander Martin & Oskar Schneider, 2017. "A comparison of performance metrics for balancing the power consumption of trains in a railway network by slight timetable adaptation," Public Transport, Springer, vol. 9(1), pages 95-113, July.
    15. Mo, Pengli & D’Ariano, Andrea & Yang, Lixing & Veelenturf, Lucas P. & Gao, Ziyou, 2021. "An exact method for the integrated optimization of subway lines operation strategies with asymmetric passenger demand and operating costs," Transportation Research Part B: Methodological, Elsevier, vol. 149(C), pages 283-321.
    16. Hörsting, Lena & Cleophas, Catherine, 2023. "Scheduling shared passenger and freight transport on a fixed infrastructure," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1158-1169.
    17. Canca, David & Barrena, Eva & De-Los-Santos, Alicia & Andrade-Pineda, José Luis, 2016. "Setting lines frequency and capacity in dense railway rapid transit networks with simultaneous passenger assignment," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 251-267.
    18. Xue, Hongjiao & Jia, Limin & Li, Jian & Guo, Jianyuan, 2022. "Jointly optimized demand-oriented train timetable and passenger flow control strategy for a congested subway line under a short-turning operation pattern," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 593(C).
    19. Martello, Silvano & Pinto Paixão, José M., 2012. "A look at the past and present of optimization – An editorial," European Journal of Operational Research, Elsevier, vol. 219(3), pages 638-640.
    20. David Schindl & Nicolas Zufferey, 2015. "A learning tabu search for a truck allocation problem with linear and nonlinear cost components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(1), pages 32-45, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:1035-:d:1072856. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.