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On some optimal control problems governed by a state equation with memory

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Date
2008
Dewey
Probabilités et mathématiques appliquées
Sujet
Optimization and Control
Journal issue
ESAIM. COCV
Volume
14
Number
4
Publication date
2008
Article pages
725-743
Publisher
EDP Sciences
DOI
http://dx.doi.org/10.1051/cocv:2008005
URI
https://basepub.dauphine.fr/handle/123456789/1012
Collections
  • CEREMADE : Publications
Metadata
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Author
Carlier, Guillaume
Tahraoui, Rabah
Type
Article accepté pour publication ou publié
Abstract (EN)
The aim of this paper is to study problems of the form: $inf_{(u\in V)} J(u)$ with $J(u):=\int_0^1 L(s,y_u(s),u(s)){\rm d}s+g(y_u(1))$ where V is a set of admissible controls and y u is the solution of the Cauchy problem: $\dot{x}(t) = \langle f(.,x(.)), \nu_t \rangle + u(t), t \in (0,1)$ , $x(0) = x_{\rm 0}$ and each $\nu_t$ is a nonnegative measure with support in [0,t]. After studying the Cauchy problem, we establish existence of minimizers, optimality conditions (in particular in the form of a nonlocal version of the Pontryagin principle) and prove some regularity results. We also consider the more general case where the control also enters the dynamics in a nonlocal way.

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