[Approximation semi-décentralisée d'un contrôle optimal pour des equations aux dérivées partielles dans un domaine borné]
Nous présentons une méthode de calcul de contrôle optimal pour des systèmes distribués linéaires. Sa construction repose sur le calcul fonctionnel des opérateurs auto-adjoints et sur la formule de représentation de Dunford–Schwartz. Elle est conçue pour des architectures de calcul à très fine granularité avec coordination semi-décentralisée. Enfin, elle est illustrée par un exemple portant sur la stabilisation des vibrations dans une matrice de micro-cantilevers.
We present a computational method for the optimal control of linear distributed systems. Its derivation is based on the functional calculus of self-adjoint operators, and on the Dunford–Schwartz representation formula. It has been devised to be implementable on very fine grained computing processors with semi-decentralized coordination. Finally, it is illustrated by an example related to vibration stabilization of a micro-cantilever array.
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Publié le :
Mots-clés : Instabilité, Contrôle optimal distribué, Contrôle décentralisé, Modèle multiéchelle, Matrice de micro-cantilevers
Michel Lenczner 1 ; Youssef Yakoubi 2
@article{CRMECA_2009__337_4_245_0,
author = {Michel Lenczner and Youssef Yakoubi},
title = {Semi-decentralized approximation of optimal control for partial differential equations in bounded domains},
journal = {Comptes Rendus. M\'ecanique},
pages = {245--250},
publisher = {Elsevier},
volume = {337},
number = {4},
year = {2009},
doi = {10.1016/j.crme.2009.03.013},
language = {en},
}
TY - JOUR AU - Michel Lenczner AU - Youssef Yakoubi TI - Semi-decentralized approximation of optimal control for partial differential equations in bounded domains JO - Comptes Rendus. Mécanique PY - 2009 SP - 245 EP - 250 VL - 337 IS - 4 PB - Elsevier DO - 10.1016/j.crme.2009.03.013 LA - en ID - CRMECA_2009__337_4_245_0 ER -
%0 Journal Article %A Michel Lenczner %A Youssef Yakoubi %T Semi-decentralized approximation of optimal control for partial differential equations in bounded domains %J Comptes Rendus. Mécanique %D 2009 %P 245-250 %V 337 %N 4 %I Elsevier %R 10.1016/j.crme.2009.03.013 %G en %F CRMECA_2009__337_4_245_0
Michel Lenczner; Youssef Yakoubi. Semi-decentralized approximation of optimal control for partial differential equations in bounded domains. Comptes Rendus. Mécanique, Volume 337 (2009) no. 4, pp. 245-250. doi : 10.1016/j.crme.2009.03.013. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2009.03.013/
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