no. 2
Optimal Control
Description of all privileged coordinates in the homogeneous approximation problem for nonlinear control systems
[Description de toutes les coordonnées privilégiées dans le problème d'approximation homogène pour les systèmes contrôlés non linéaires]

Présenté par : Pierre-Louis Lions

Sklyar, Grigory1 ; Ignatovich, Svetlana2
1 University of Szczecin, Wielkopolska str., 15, 70-451, Szczecin, Poland
2 Kharkov National University, Svoboda sqr. 4, Kharkov, 61077, Ukraine
Comptes Rendus. Mathématique, Tome 344 (2007) no. 2, pp. 109-114.

Dans le problème d'approximation homogène pour des systèmes contrôlés affines les coordonnées privilégiées sont celles dans lesquelles le système a une forme « triangulaire » qui permet de trouver un système d'approximation. Nous donnons les conditions nécessaires et suffisantes pour que des coordonnées soient privilégiées. Nous utilisons une technique algébrique basée sur la représentation par des séries de systèmes de commande affines.

In a homogeneous approximation problem for affine control systems, privileged coordinates are those in which the system takes a ‘triangular’ form allowing one to find an approximating system. We give the necessary and sufficient conditions for coordinates to be privileged. We apply an algebraic technique based on the series representation of affine control systems.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.11.016
Sklyar, Grigory 1 ; Ignatovich, Svetlana 2

1 University of Szczecin, Wielkopolska str., 15, 70-451, Szczecin, Poland
2 Kharkov National University, Svoboda sqr. 4, Kharkov, 61077, Ukraine 
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Sklyar, Grigory; Ignatovich, Svetlana. Description of all privileged coordinates in the homogeneous approximation problem for nonlinear control systems. Comptes Rendus. Mathématique, Tome 344 (2007) no. 2, pp. 109-114. doi : 10.1016/j.crma.2006.11.016. http://www.numdam.org/articles/10.1016/j.crma.2006.11.016/

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