[Une condition de type Kalman pour la contrôlabilité stochastique approchée]
On s'intéresse à la propriété de contrôlabilité approchée pour une équation différentielle stochastique linéaire. Pour le contrôle déterministe, il existe une condition nécessaire et suffisante appelée condition de Kalman. Pour le cas stochastique, des critères sont connus soit dans le cas où le contrôle agit pleinement sur le bruit, soit dans le cas où il n'y a aucun contrôle sur le bruit. Nous proposons une généralisation de la condition de Kalman pour le cas général.
We are interested in the approximate controllability property for a linear stochastic differential equation. For deterministic control necessary and sufficient criterion exists and is called Kalman condition. In the stochastic framework criteria are already known either when the control fully acts on the noise coefficient or when there is no control acting on the noise. We propose a generalization of Kalman condition for the general case.
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@article{CRMATH_2008__346_3-4_183_0,
author = {Goreac, Dan},
title = {A {Kalman-type} condition for stochastic approximate controllability},
journal = {Comptes Rendus. Math\'ematique},
pages = {183--188},
publisher = {Elsevier},
volume = {346},
number = {3-4},
year = {2008},
doi = {10.1016/j.crma.2007.12.008},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2007.12.008/}
}
TY - JOUR AU - Goreac, Dan TI - A Kalman-type condition for stochastic approximate controllability JO - Comptes Rendus. Mathématique PY - 2008 SP - 183 EP - 188 VL - 346 IS - 3-4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2007.12.008/ DO - 10.1016/j.crma.2007.12.008 LA - en ID - CRMATH_2008__346_3-4_183_0 ER -
%0 Journal Article %A Goreac, Dan %T A Kalman-type condition for stochastic approximate controllability %J Comptes Rendus. Mathématique %D 2008 %P 183-188 %V 346 %N 3-4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2007.12.008/ %R 10.1016/j.crma.2007.12.008 %G en %F CRMATH_2008__346_3-4_183_0
Goreac, Dan. A Kalman-type condition for stochastic approximate controllability. Comptes Rendus. Mathématique, Tome 346 (2008) no. 3-4, pp. 183-188. doi : 10.1016/j.crma.2007.12.008. http://www.numdam.org/articles/10.1016/j.crma.2007.12.008/
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