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Necessary Conditions for Impulsive Nonlinear Optimal Control Problems without a priori Normality Assumptions

Author

Listed:
  • A. Arutyunov

    (People Friendship University of Russia)

  • V. Dykhta

    (Baikal State University of Economy and Law)

  • F. Lobo Pereira

    (University of Porto)

Abstract

First-order and second-order necessary conditions of optimality for an impulsive control problem that remain informative for abnormal control processes are presented and derived. One of the main features of these conditions is that no a priori normality assumptions are required. This feature follows from the fact that these conditions rely on an extremal principle which is proved for an abstract minimization problem with equality constraints, inequality constraints, and constraints given by an inclusion in a convex cone. Two simple examples illustrate the power of the main result.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:124:y:2005:i:1:d:10.1007_s10957-004-6465-x
    DOI: 10.1007/s10957-004-6465-x
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    Cited by:

    1. 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.
    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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