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Normality and Nondegeneracy for Optimal Control Problems with State Constraints

Author

Listed:
  • Fernando A. C. C. Fontes

    (Universidade do Porto)

  • Hélène Frankowska

    (Sorbonne Universits, UPMC Univ Paris 06, Univ Paris Diderot)

Abstract

In this paper, we investigate normal and nondegenerate forms of the maximum principle for optimal control problems with state constraints. We propose new constraint qualifications guaranteeing nondegeneracy and normality that have to be checked on smaller sets of points of an optimal trajectory than those in known sufficient conditions. In fact, the constraint qualifications proposed impose the existence of an inward pointing velocity just on the instants of time for which the optimal trajectory has an outward pointing velocity.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:166:y:2015:i:1:d:10.1007_s10957-015-0704-1
    DOI: 10.1007/s10957-015-0704-1
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    Cited by:

    1. Monica Motta & Caterina Sartori, 2020. "Normality and Nondegeneracy of the Maximum Principle in Optimal Impulsive Control Under State Constraints," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 44-71, April.
    2. Giovanni Fusco & Monica Motta, 2024. "Abnormality and Strict-Sense Minimizers That Are Not Extended Minimizers," Mathematics, MDPI, vol. 12(7), pages 1-21, March.
    3. Vu Thi Huong & Jen-Chih Yao & Nguyen Dong Yen, 2021. "Optimal Economic Growth Models with Nonlinear Utility Functions," Journal of Optimization Theory and Applications, Springer, vol. 188(2), pages 571-596, February.
    4. Farhad Hasankhani & Amin Khademi, 2021. "Is it Time to Include Post‐Transplant Survival in Heart Transplantation Allocation Rules?," Production and Operations Management, Production and Operations Management Society, vol. 30(8), pages 2653-2671, August.
    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. Luís Tiago Paiva & Fernando A. C. C. Fontes, 2018. "Optimal Control Algorithms with Adaptive Time-Mesh Refinement for Kite Power Systems," Energies, MDPI, vol. 11(3), pages 1-17, February.

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