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A Survey on Regularity Conditions for State-Constrained Optimal Control Problems and the Non-degenerate Maximum Principle

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  • Aram Arutyunov

    (V.A. Trapeznikov Institute of Control Sciences of RAS)

  • Dmitry Karamzin

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

Abstract

A survey on the theory of maximum principle for state-constrained optimal control problems is presented. The focus is on such issues as regularity and controllability conditions, non-degeneracy and normality of the maximum principle, and on the continuity of the measure multiplier.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:184:y:2020:i:3:d:10.1007_s10957-019-01623-7
    DOI: 10.1007/s10957-019-01623-7
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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. Giovanni Colombo & Boris Mordukhovich & Dao Nguyen, 2019. "Optimal Control of Sweeping Processes in Robotics and Traffic Flow Models," Journal of Optimization Theory and Applications, Springer, vol. 182(2), pages 439-472, August.
    3. 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.
    4. A. D. Ioffe, 1984. "Necessary Conditions in Nonsmooth Optimization," Mathematics of Operations Research, INFORMS, vol. 9(2), pages 159-189, May.
    5. Nguyen D. Hoang & Boris S. Mordukhovich, 2019. "Extended Euler–Lagrange and Hamiltonian Conditions in Optimal Control of Sweeping Processes with Controlled Moving Sets," Journal of Optimization Theory and Applications, Springer, vol. 180(1), pages 256-289, January.
    6. Fernando A. C. C. Fontes & Hélène Frankowska, 2015. "Normality and Nondegeneracy for Optimal Control Problems with State Constraints," Journal of Optimization Theory and Applications, Springer, vol. 166(1), pages 115-136, July.
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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. Jorge Becerril & Cristopher Hermosilla, 2022. "Optimality Conditions for Linear-Convex Optimal Control Problems with Mixed Constraints," Journal of Optimization Theory and Applications, Springer, vol. 194(3), pages 795-820, September.
    3. Askhat Diveev & Elizaveta Shmalko & Vladimir Serebrenny & Peter Zentay, 2020. "Fundamentals of Synthesized Optimal Control," Mathematics, MDPI, vol. 9(1), pages 1-18, December.

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