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

Guillaume Carlier; Rabah Tahraoui

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

- Volume: 14, Issue: 4, page 725-743
- ISSN: 1292-8119

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topCarlier, Guillaume, and Tahraoui, Rabah. "On some optimal control problems governed by a state equation with memory." ESAIM: Control, Optimisation and Calculus of Variations 14.4 (2008): 725-743. <http://eudml.org/doc/250320>.

@article{Carlier2008,

abstract = {
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 yu 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.
},

author = {Carlier, Guillaume, Tahraoui, Rabah},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Optimal control; memory; optimal control},

language = {eng},

month = {1},

number = {4},

pages = {725-743},

publisher = {EDP Sciences},

title = {On some optimal control problems governed by a state equation with memory},

url = {http://eudml.org/doc/250320},

volume = {14},

year = {2008},

}

TY - JOUR

AU - Carlier, Guillaume

AU - Tahraoui, Rabah

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

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2008/1//

PB - EDP Sciences

VL - 14

IS - 4

SP - 725

EP - 743

AB -
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 yu 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.

LA - eng

KW - Optimal control; memory; optimal control

UR - http://eudml.org/doc/250320

ER -

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