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Comptes Rendus Mathématique
Volume 343, n° 7
pages 473-478 (octobre 2006)
Doi : 10.1016/j.crma.2006.09.005
Received : 23 February 2006 ;  accepted : 5 September 2006
Conditions dʼoptimalité du second ordre nécessaires ou suffisantes pour les problèmes de commande optimale avec une contrainte sur lʼétat et une commande scalaires
No-gap second-order optimality conditions for optimal control problems with a single state constraint and control
 

J. Frédéric Bonnans , Audrey Hermant
INRIA-Futurs et CMAP, École polytechnique, 91128 Palaiseau cedex, France 

Résumé

Dans cette Note, nous étudions un problème de commande optimale avec une commande scalaire et une contrainte sur lʼétat scalaire dʼordre quelconque. Les instants de jonction sont supposés en nombre fini. Nous obtenons des conditions dʼoptimalité du second ordre nécessaires ou suffisantes, qui permettent de caractériser la croissance quadratique. Pour citer cet article : J.F. Bonnans, A. Hermant, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

The full text of this article is available in PDF format.
Abstract

This Note deals with optimal control problems with only one control variable and one state constraint, of arbitrary order. We consider the case of finitely many boundary arcs and touch times. We obtain a no-gap theory of second-order conditions, allowing us to characterize second-order quadratic growth. To cite this article: J.F. Bonnans, A. Hermant, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

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