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Normality and Nondegeneracy of the Maximum Principle in Optimal Impulsive Control Under State Constraints

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  • Monica Motta

    (University of Padua)

  • Caterina Sartori

    (University of Padua)

Abstract

We investigate nondegenerate and normal forms of the maximum principle for general, free end-time, impulsive optimal control problems with state and endpoint constraints. We introduce constraint qualifications sufficient to avoid degeneracy or abnormality phenomena, which do not require any convexity and impose the existence of an inward pointing velocity just on the subset of times, in which the extended optimal trajectory has an outward pointing velocity (w.r.t. the state constraint). These conditions extend to impulsive problems some conditions, recently proposed by F. Fontes and H. Frankowska, for conventional optimization problems. The nontriviality of this extension is illustrated through some examples.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:185:y:2020:i:1:d:10.1007_s10957-020-01641-w
    DOI: 10.1007/s10957-020-01641-w
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    References listed on IDEAS

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    1. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(5), pages 777-788, October.
    2. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(1), pages 151-160, February.
    3. 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.
    4. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(4), pages 629-637, August.
    5. 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.
    6. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(3), pages 427-432, June.
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