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Value function and optimality conditions for semilinear control problems

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Date
1992
Dewey
Probabilités et mathématiques appliquées
Sujet
Optimal control; Distributed parameter systems; Dynamic programming; Optimality conditions; Strongly continuous semigroups; Nonsmooth analysis
Journal issue
Applied Mathematics and Optimization
Volume
26
Number
2
Publication date
1992
Article pages
139-169
Publisher
Springer
DOI
http://dx.doi.org/http://dx;doi.org/10.1007/BF01189028
URI
https://basepub.dauphine.fr/handle/123456789/14443
Collections
  • CEREMADE : Publications
Metadata
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Author
Cannarsa, Piermarco
Frankowska, Halina
Type
Article accepté pour publication ou publié
Abstract (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.

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