Optimal control for distributed systems subject to null-controllability. Application to discriminating sentinels

Ousseynou Nakoulima

ESAIM: Control, Optimisation and Calculus of Variations (2007)

  • Volume: 13, Issue: 4, page 623-638
  • ISSN: 1292-8119

Abstract

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We consider a distributed system in which the state q is governed by a parabolic equation and a pair of controls v = (h,k) where h and k play two different roles: the control k is of controllability type while h expresses that the state q does not move too far from a given state. Therefore, it is natural to introduce the control point of view. In fact, there are several ways to state and solve optimal control problems with a pair of controls h and k, in particular the Least Squares method with only one criteria for the pair (h,k) or the Pareto Optimal Control for multicriteria problems. We propose here to use the notion of Hierarchic Control. This notion assumes that we have two controls h, k where h will be the leader while k will be the follower. The main tool used to solve the null-controllability problem with constraints on the follower is an observability inequality of Carleman type which is “adapted” to the constraints. The obtained results are applied to the sentinels theory of Lions [Masson (1992)].

How to cite

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Nakoulima, Ousseynou. "Optimal control for distributed systems subject to null-controllability. Application to discriminating sentinels." ESAIM: Control, Optimisation and Calculus of Variations 13.4 (2007): 623-638. <http://eudml.org/doc/249999>.

@article{Nakoulima2007,
abstract = { We consider a distributed system in which the state q is governed by a parabolic equation and a pair of controls v = (h,k) where h and k play two different roles: the control k is of controllability type while h expresses that the state q does not move too far from a given state. Therefore, it is natural to introduce the control point of view. In fact, there are several ways to state and solve optimal control problems with a pair of controls h and k, in particular the Least Squares method with only one criteria for the pair (h,k) or the Pareto Optimal Control for multicriteria problems. We propose here to use the notion of Hierarchic Control. This notion assumes that we have two controls h, k where h will be the leader while k will be the follower. The main tool used to solve the null-controllability problem with constraints on the follower is an observability inequality of Carleman type which is “adapted” to the constraints. The obtained results are applied to the sentinels theory of Lions [Masson (1992)]. },
author = {Nakoulima, Ousseynou},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Heat equation; optimal control; controllability; Carleman inequalities; sentinels; Pareto optimal control},
language = {eng},
month = {9},
number = {4},
pages = {623-638},
publisher = {EDP Sciences},
title = {Optimal control for distributed systems subject to null-controllability. Application to discriminating sentinels},
url = {http://eudml.org/doc/249999},
volume = {13},
year = {2007},
}

TY - JOUR
AU - Nakoulima, Ousseynou
TI - Optimal control for distributed systems subject to null-controllability. Application to discriminating sentinels
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2007/9//
PB - EDP Sciences
VL - 13
IS - 4
SP - 623
EP - 638
AB - We consider a distributed system in which the state q is governed by a parabolic equation and a pair of controls v = (h,k) where h and k play two different roles: the control k is of controllability type while h expresses that the state q does not move too far from a given state. Therefore, it is natural to introduce the control point of view. In fact, there are several ways to state and solve optimal control problems with a pair of controls h and k, in particular the Least Squares method with only one criteria for the pair (h,k) or the Pareto Optimal Control for multicriteria problems. We propose here to use the notion of Hierarchic Control. This notion assumes that we have two controls h, k where h will be the leader while k will be the follower. The main tool used to solve the null-controllability problem with constraints on the follower is an observability inequality of Carleman type which is “adapted” to the constraints. The obtained results are applied to the sentinels theory of Lions [Masson (1992)].
LA - eng
KW - Heat equation; optimal control; controllability; Carleman inequalities; sentinels; Pareto optimal control
UR - http://eudml.org/doc/249999
ER -

References

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