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The Maximum Principle for Optimal Control Problems with State Constraints by R.V. Gamkrelidze: Revisited

Author

Listed:
  • A. V. Arutyunov

    (Peoples’ Friendship University of Russia)

  • D. Y. Karamzin

    (Russian Academy of Sciences
    University of Porto)

  • F. L. Pereira

    (Institute for Systems & Robotics)

Abstract

A maximum principle in the form given by R.V. Gamkrelidze is obtained, although without a priori regularity assumptions to be satisfied by the optimal trajectory. After its formulation and proof, we propose various regularity concepts that guarantee, in one sense or another, the nondegeneracy of the maximum principle. Finally, we show how the already known first-order necessary conditions can be deduced from the proposed theorem.

Suggested Citation

  • A. V. Arutyunov & D. Y. Karamzin & F. L. Pereira, 2011. "The Maximum Principle for Optimal Control Problems with State Constraints by R.V. Gamkrelidze: Revisited," Journal of Optimization Theory and Applications, Springer, vol. 149(3), pages 474-493, June.
    • Handle: RePEc:spr:joptap:v:149:y:2011:i:3:d:10.1007_s10957-011-9807-5
    DOI: 10.1007/s10957-011-9807-5
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    Citations

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    Cited by:

    1. Fernando Lobo Pereira & Nathalie T. Khalil, 2022. "A Maximum Principle for a Time-Optimal Bilevel Sweeping Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 192(3), pages 1022-1051, March.
    2. Adam Korytowski & Maciej Szymkat, 2021. "Necessary Optimality Conditions for a Class of Control Problems with State Constraint," Games, MDPI, vol. 12(1), pages 1-22, January.
    3. Lohéac, Jérôme & Varma, Vineeth Satheeskumar & Morărescu, Irinel Constantin, 2022. "Time optimal control for a mobile robot with a communication objective," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 96-120.
    4. Dmitry Karamzin & Fernando Lobo Pereira, 2019. "On a Few Questions Regarding the Study of State-Constrained Problems in Optimal Control," Journal of Optimization Theory and Applications, Springer, vol. 180(1), pages 235-255, January.
    5. Aram Arutyunov & Dmitry Karamzin, 2020. "A Survey on Regularity Conditions for State-Constrained Optimal Control Problems and the Non-degenerate Maximum Principle," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 697-723, March.
    6. Dmitry Karamzin, 2018. "Comments on Paper “On the Relation Between Two Approaches to Necessary Optimality Conditions in Problems with State Constraints”," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 358-362, October.
    7. A. V. Arutyunov & D. Yu. Karamzin & F. L. Pereira, 2015. "State Constraints in Impulsive Control Problems: Gamkrelidze-Like Conditions of Optimality," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 440-459, August.
    8. Andrei Dmitruk & Ivan Samylovskiy, 2017. "On the Relation Between Two Approaches to Necessary Optimality Conditions in Problems with State Constraints," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 391-420, May.

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