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No-gap second-order optimality conditions for optimal control problems with a single state constraint and control. (Conditions d’optimalité du second ordre nécessaires ou suffisantes pour les problèmes de commande optimale avec une contrainte sur l’état et une commande scalaires.) (French. Abridged English version) Zbl 1101.49020

Summary: 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.

MSC:

49K27 Optimality conditions for problems in abstract spaces
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[1] J.F. Bonnans, A. Hermant, No gap second order optimality conditions for optimal control problems with a single state constraint and control, INRIA Report 5837 (2006), Mathematical Programming, in press; J.F. Bonnans, A. Hermant, No gap second order optimality conditions for optimal control problems with a single state constraint and control, INRIA Report 5837 (2006), Mathematical Programming, in press · Zbl 1101.49020
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