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

Lassana Samassi; Rabah Tahraoui

ESAIM: Control, Optimisation and Calculus of Variations (2008)

  • Volume: 14, Issue: 2, page 381-409
  • ISSN: 1292-8119

Abstract

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The aim of this paper is to give a general idea to state optimality conditions of control problems in the following form: inf ( u , v ) ∈ 𝒰 a d ∫ 0 1 f t , u ( θ v ( t ) ) , u ' ( t ) , v ( t ) d t , (1) where 𝒰 a d is a set of admissible controls and θ v is the solution of the following equation: { d θ ( t ) d t = g ( t , θ ( t ) , v ( t ) ) , t ∈ [ 0 , 1 ] ; θ ( 0 ) = θ 0 , θ ( t ) ∈ [ 0 , 1 ] ∀ t . (2). The results are nonlocal and new.

How to cite

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Samassi, Lassana, and Tahraoui, Rabah. "How to state necessary optimality conditions for control problems with deviating arguments?." ESAIM: Control, Optimisation and Calculus of Variations 14.2 (2008): 381-409. <http://eudml.org/doc/250383>.

@article{Samassi2008,
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. },
author = {Samassi, Lassana, Tahraoui, Rabah},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Functionals with deviating arguments; optimal control; Euler-Lagrange equation; financial market; functionals with deviating arguments},
language = {eng},
month = {3},
number = {2},
pages = {381-409},
publisher = {EDP Sciences},
title = {How to state necessary optimality conditions for control problems with deviating arguments?},
url = {http://eudml.org/doc/250383},
volume = {14},
year = {2008},
}

TY - JOUR
AU - Samassi, Lassana
AU - Tahraoui, Rabah
TI - How to state necessary optimality conditions for control problems with deviating arguments?
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2008/3//
PB - EDP Sciences
VL - 14
IS - 2
SP - 381
EP - 409
AB - 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.
LA - eng
KW - Functionals with deviating arguments; optimal control; Euler-Lagrange equation; financial market; functionals with deviating arguments
UR - http://eudml.org/doc/250383
ER -

References

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  16. L. Samassi and R. Tahraoui, Comment établir des conditions nécessaires d'optimalité dans les problèmes de contrôle dont certains arguments sont déviés ? C.R. Acad. Sci. Paris Ser338 (2004) 611–616.  
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