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On a Few Questions Regarding the Study of State-Constrained Problems in Optimal Control

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  • Dmitry Karamzin

    (Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences)

  • Fernando Lobo Pereira

    (University of Porto)

Abstract

The article is focused on the investigation of the necessary optimality conditions in the form of Pontryagin’s maximum principle for optimal control problems with state constraints. A number of results on this topic, which refine the existing ones, are presented. These results concern the nondegenerate maximum principle under weakened controllability assumptions and also the continuity of the measure Lagrange multiplier.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:180:y:2019:i:1:d:10.1007_s10957-018-1394-2
    DOI: 10.1007/s10957-018-1394-2
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    References listed on IDEAS

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    1. 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.
    2. A. D. Ioffe, 1984. "Necessary Conditions in Nonsmooth Optimization," Mathematics of Operations Research, INFORMS, vol. 9(2), pages 159-189, May.
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    Cited by:

    1. 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.

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