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How to state necessary optimality conditions for control problems with deviating arguments?

Published online by Cambridge University Press:  20 March 2008

Lassana Samassi  and
Rabah Tahraoui
Lassana Samassi
Affiliation:
Ceremade, Université Paris IX-Dauphine, France; samassi@ceremade.dauphine.fr; tahraoui@ceremade.dauphine.fr
Rabah Tahraoui
Affiliation:
Ceremade, Université Paris IX-Dauphine, France; samassi@ceremade.dauphine.fr; tahraoui@ceremade.dauphine.fr
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Abstract

The aim of this paper is to give a general idea to state optimality conditions of control problems in the following form: ${\displaystyle\inf_{{\displaystyle(u,v)\in {\cal U}_{ad}}} \int_{0}^{1} f\left(t, u(\theta_v(t)),u^{\prime}(t),v(t)\right){\rm d}t}$, (1) where ${\cal U}_{ad} $ is a set of admissible controls and $\theta_v$ is the solution of the following equation: $\{ \frac{{\rm d}\theta(t)}{{\rm d}t}=g(t,\theta(t),v(t)), t\in [0,1]$ ; $\displaystyle\theta(0)=\theta_0, \theta(t)\in [0,1] \forall t$. (2). The results are nonlocal and new.

Keywords

Functionals with deviating argumentsoptimal controlEuler-Lagrange equationfinancial market
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 14 , Issue 2 , April 2008 , pp. 381 - 409
Copyright
© EDP Sciences, SMAI, 2008

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