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Comptes Rendus Mathématique
Volume 346, n° 3-4
pages 183-188 (février 2008)
Doi : 10.1016/j.crma.2007.12.008
Received : 26 February 2007 ;  accepted : 11 December 2007
A Kalman-type condition for stochastic approximate controllability
Une condition de type Kalman pour la contrôlabilité stochastique approchée
 

Dan Goreac
Laboratoire de mathématiques, Unité CNRS UMR 6205, Université de Bretagne Occidentale, 6, avenue Victor-LeGorgeu, B.P. 809, 29285 Brest cedex, France 

Abstract

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. To cite this article: D. Goreac, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

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Résumé

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. Pour citer cet article : D. Goreac, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

The full text of this article is available in PDF format.


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