Optimal Control/Probability Theory
A Kalman-type condition for stochastic approximate controllability
Comptes Rendus. Mathématique, Volume 346 (2008) no. 3-4, pp. 183-188.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2007.12.008
Goreac, Dan 1

1 Laboratoire de mathématiques, Unité CNRS UMR 6205, Université de Bretagne Occidentale, 6, avenue Victor-LeGorgeu, B.P. 809, 29285 Brest cedex, France
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Goreac, Dan. A Kalman-type condition for stochastic approximate controllability. Comptes Rendus. Mathématique, Volume 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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