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State Constraints in Impulsive Control Problems: Gamkrelidze-Like Conditions of Optimality

Author

Listed:
  • A. V. Arutyunov

    (Peoples’ Friendship University of Russia)

  • D. Yu. Karamzin

    (Computing Centre of the Russian Academy of Sciences)

  • F. L. Pereira

    (University of Porto)

Abstract

An impulsive control problem with state constraints is considered. A Pontryagin maximum principle in the framework of R.V. Gamkrelidze is derived, being its proof based on a certain penalization technique and on the application of Ekeland’s variational principle. This approach is distinct from the more usual ones in Impulsive Control theory based on a reduction to a conventional control problem and exhibits the advantage of allowing to address problems with dynamics which are merely measurable in the time variable. Controllability assumptions to ensure the non-degeneracy of the conditions are provided in the impulsive control context. An example demonstrating the significance of the conditions is given.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:166:y:2015:i:2:d:10.1007_s10957-014-0690-8
    DOI: 10.1007/s10957-014-0690-8
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    References listed on IDEAS

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    1. A. Arutyunov & V. Dykhta & F. Lobo Pereira, 2005. "Necessary Conditions for Impulsive Nonlinear Optimal Control Problems without a priori Normality Assumptions," Journal of Optimization Theory and Applications, Springer, vol. 124(1), pages 55-77, January.
    2. 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.
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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.

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