. Dans-le-premier-chapitre, si et seulement si les conditions de régularité dim D (i) (x 0 ) = dim D i (x 0 ), pour 0 ? i ? n, sont satisfaites Ceci répondrépondà la question posée par Martin et Rouchon [39] (voir aussi [40]) pour la x-platitude. Ensuite , nous avons donné des conditions nécessaires et suffisantes vérifiables (Theorème 1.3.2 et 1.3.3) pour qu'une paire de fonctions données (? 1 , ? 2 ) forme une x-sortie plate du système ? avec deux contrôles qui estéquivalentestéquivalent au système cha??nécha??né (système de contact canonique sur J n (R 1 , R 1 )). Nous avons aussi décrit le lieu singulier de cette x-sorties plate. Notons C n?1 la distribution caractéristique de D (n?1) et g un champ de vecteurs dans D tel que g(x 0 ) ? C n?1 (x 0 ) Nous avons montré qu'´ etant donné une fonction lisse ? 1 telle que L c ? 1 = 0 De plus, nous avonsétudiéavonsétudié la propriété de la platitude des systèmes avec deux contrôles.Premì erement

. Dans-ledeuxì-eme-chapitre, nous avonsétudiéavonsétudié le systèmè a n-barres dans l'espace R m+1 qui généralise le système du robot mobile avec remorques sur le plan, Nous avons introduit un modèle cinématique de ce système sans utiliser les variables d'angle

L. Résultats-principaux-sont-les-suivants, Le systèmè a n-barres dans R m+1 est localementéquivalentlocalementéquivalent au système m-cha??nécha??né (i.e., système de contact canonique sur J n (R 1 , R m )) en tous les points réguliers que nous avons caractérisés. Nous avons aussi References [1] C. Altafini. Some properties of the general n-Trailer, International Journal of Control, vol.74, issue.1 4, pp.409-424, 2001.

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