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Value function and optimality conditions for semilinear control problems

Cannarsa, Piermarco; Frankowska, Halina (1992), Value function and optimality conditions for semilinear control problems, Applied Mathematics and Optimization, 26, 2, p. 139-169. http://dx;doi.org/10.1007/BF01189028

Type
Article accepté pour publication ou publié
Date
1992
Nom de la revue
Applied Mathematics and Optimization
Volume
26
Numéro
2
Éditeur
Springer
Pages
139-169
Identifiant publication
Métadonnées
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Auteur(s)
Cannarsa, Piermarco
Frankowska, Halina
Résumé (EN)
This paper is concerned with optimal control problems of Mayer and Bolza type for systems governed by a semilinear state equationx′(t)=Ax(t) + f(t, x(t), u(t)), u(t) ε U, whereA is the infinitesimal generator of a strongly continuous semigroup in a Banach spaceX. We prove necessary and sufficient conditions for optimality and then use these conditions to investigate properties of the value function related to superdifferentials. Conversely, we use the value function to obtain criteria for optimality and feedback systems.
Mots-clés
Optimal control; Distributed parameter systems; Dynamic programming; Optimality conditions; Strongly continuous semigroups; Nonsmooth analysis