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. Lian, Deheng & Mo, Pengli & D’Ariano, Andrea & Gao, Ziyou & Yang, Lixing, 2024. "Energy-saving time allocation strategy with uncertain dwell times in urban rail transit: Two-stage stochastic model and nested dynamic programming framework," European Journal of Operational Research, Elsevier, vol. 317(1), pages 219-242.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Gábor Maróti, 2017. "A branch-and-bound approach for robust railway timetabling," Public Transport, Springer, vol. 9(1), pages 73-94, July.
    8. Hartleb, Johann & Schmidt, Marie, 2022. "Railway timetabling with integrated passenger distribution," European Journal of Operational Research, Elsevier, vol. 298(3), pages 953-966.
    9. 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.
    10. 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).
    11. 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.
    12. 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.
    13. Zhang, Chuntian & Gao, Yuan & Yang, Lixing & Gao, Ziyou & Qi, Jianguo, 2020. "Joint optimization of train scheduling and maintenance planning in a railway network: A heuristic algorithm using Lagrangian relaxation," Transportation Research Part B: Methodological, Elsevier, vol. 134(C), pages 64-92.
    14. Xie, J. & Wong, S.C. & Zhan, S. & Lo, S.M. & Chen, Anthony, 2020. "Train schedule optimization based on schedule-based stochastic passenger assignment," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 136(C).
    15. Soha Saad & Florence Ossart & Jean Bigeon & Etienne Sourdille & Harold Gance, 2021. "Global Sensitivity Analysis Applied to Train Traffic Rescheduling: A Comparative Study," Energies, MDPI, vol. 14(19), pages 1-29, October.
    16. Liang, Jinpeng & Zang, Guangzhi & Liu, Haitao & Zheng, Jianfeng & Gao, Ziyou, 2023. "Reducing passenger waiting time in oversaturated metro lines with passenger flow control policy," Omega, Elsevier, vol. 117(C).
    17. Högdahl, Johan & Bohlin, Markus & Fröidh, Oskar, 2019. "A combined simulation-optimization approach for minimizing travel time and delays in railway timetables," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 192-212.
    18. Maosheng Li & Zhengqiu Liu & Yonghong Zhang & Weijun Liu & Feng Shi, 2017. "Distribution analysis of train interval journey time employing the censored model with shifting character," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(4), pages 715-733, March.
    19. Andreas Bärmann & Alexander Martin & Oskar Schneider, 2021. "Efficient Formulations and Decomposition Approaches for Power Peak Reduction in Railway Traffic via Timetabling," Transportation Science, INFORMS, vol. 55(3), pages 747-767, May.
    20. Taslimi, Bijan & Babaie Sarijaloo, Farnaz & Liu, Hongcheng & Pardalos, Panos M., 2022. "A novel mixed integer programming model for freight train travel time estimation," European Journal of Operational Research, Elsevier, vol. 300(2), pages 676-688.

    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.