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

A. V. Arutyunov (), D. Yu. Karamzin () and F. L. Pereira ()
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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

Journal of Optimization Theory and Applications, 2015, vol. 166, issue 2, No 5, 440-459

Abstract: 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.

Keywords: Impulsive control; Maximum principle; State constraints; 49N25 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-014-0690-8

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