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Optimal Control Problem for Minimization of Net Energy Consumption at Metro

Author

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  • 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
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    References listed on IDEAS

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    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.
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