Inward Pointing Trajectories, Normality of the Maximum Principle and the Non Occurrence of the Lavrentieff Phenomenon in Optimal Control under State Constraints

Hélène Frankowska 1 Daniela Tonon 1
1 C&O - Equipe combinatoire et optimisation
UPMC - Université Pierre et Marie Curie - Paris 6, CNRS - Centre National de la Recherche Scientifique : FRE3232
Abstract : Journal of Convex Analysis 20 (2013), No. 4, [final page numbers not yet available] Copyright Heldermann Verlag 2013 Inward Pointing Trajectories, Normality of the Maximum Principle and the Non Occurrence of the Lavrentieff Phenomenon in Optimal Control under State Constraints Hélène Frankowska Institut de Mathématiques, Université P. et M. Curie, Case 247 -- 4 place Jussieu, 75252 Paris, France frankowska@math.jussieu.fr Daniela Tonon Institut de Mathématiques, Université P. et M. Curie, Case 247 -- 4 place Jussieu, 75252 Paris, France tonondaniela83@gmail.com It is well known that every strong local minimizer of the Bolza problem under state constraints satisfies a constrained maximum principle. In the absence of constraints qualifications the maximum principle may be abnormal, that is, not involving the cost functions. Normality of the maximum principle can be investigated by studying reachable sets of an associated linear system under linearized state constraints. In this paper we provide sufficient conditions for the existence of solutions to such system and apply them to guarantee the non occurrence of the Lavrentieff phenomenon in optimal control under state constraints.
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Journal of Convex Analysis, Heldermann, 2013, 20 (4), 〈http://www.heldermann.de/JCA/JCA20/JCA204/jca20062.htm〉
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Soumis le : mercredi 13 mars 2013 - 18:41:17
Dernière modification le : mercredi 21 mars 2018 - 18:57:28

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Hélène Frankowska, Daniela Tonon. Inward Pointing Trajectories, Normality of the Maximum Principle and the Non Occurrence of the Lavrentieff Phenomenon in Optimal Control under State Constraints. Journal of Convex Analysis, Heldermann, 2013, 20 (4), 〈http://www.heldermann.de/JCA/JCA20/JCA204/jca20062.htm〉. 〈hal-00800525〉

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