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?. ?. If-s, ?. , T. ). , ?. , T. et al., ? ? ) are all of them finite, for every T ? 0

?. If, ?. , T. ). , ?. , T. et al., (? ? ) are finite, then there exist minimizers or maximizers to every

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. Nous-montrons-qu-'un-nageur-qui-est-contrôlable-lorsqu, espace non borné, reste " presque partout " localement contrôlable lorsqu'il nage dans un domaine délimité par un mur plat ou rugueux Au contraire, nous prouvons qu'un nageur qui n'est pas capable d'atteindre toutes les directions lorsqu'il se déplace dans un domaine sans bord peutélargirpeutélargir ses directions accessibles en présence d'un mur (plat ou rugueux) Enfin, ladernì ere partie de la thèse fournit un cadrè a l'´ etude deprobì emes de contrôle optimal associés aux déplacements de nageurs ayant une dynamique sans dérive. Tout d'abord, nousétudionsnousétudions les propriétés mathématiques de plusieursprobì emes de contrôle optimal ayant des coûts fonctionnels différents (existence puis comportement). Ensuite, nous considérons les nageurs ayant deux degrés de liberté. Pour ces modèles particuliers de nageurs, nous présentons un cadre permettant d'en déduire des propriétés géométriques locales pour les solutions de certainsprobì emes de contrôle optimal