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B. , Résumé substantiel en français

, Les avantages des observateurs par intervalle sont qu'ils sont bien adaptés à la conception d'observateur dans des systèmes très incertains (si les intervalles de valeurs admissibles pour les termes inconnus sont donnés) et qu'ils sont capables de fournir des limites asymptotiquement assez serrées sur la précision de l'estimation, car l'intervalle des valeurs admissibles pour l'état à chaque instant est évalué. De plus, cette technique tire parti d'une connaissance approximative de la condition initiale et donne des informations sur l'état inconnu du système étudié à tout instant, tandis que les observateurs classiques ne fournissent qu'une information utile asymptotiquement, c'est-à-dire d'un point de vue technique, pour des valeurs temporelles suffisamment grandes. Les observateurs par intervalle, présentés dans la littérature, La thèse est consacrée à l'étude des observateurs par intervalle, qui forment une sous-classe d'estimateurs d'appartenance à un ensemble et dont la conception est basée sur la théorie des systèmes monotones, à leurs applications dans l'estimation et le contrôle de systèmes distribués incertains, ainsi qu'à l'analyse de leurs propriétés et de leurs restrictions, 2000.

E. Retardement, l'application d'une approche algébrique pour la conception par observateur dans les systèmes à retardement LPV est présentée dans Briat et al., 2011, un problème d'estimation pour les systèmes positifs avec des retards inconnus variant dans le temps est étudié dans Rami, décrit par des équations différentielles fonctionnelles. Pour ces modèles, qui sont infiniment dimensionnels contrairement aux équations différentielles ordinaires (EDO), l'analyse et la conception sont beaucoup plus compliquées et nécessitent des concepts et des algorithmes spécialement développés Richard, 2003.

, De plus, l'objectif de la thèse est d'étendre d'observateur par intervalle aux systèmes de dimension infinie, en considérant non seulement les systèmes avec des retards, mais également distribués dans les systèmes spatiaux

. Le-son, écoulement des fluides, l'élasticité ou la mécanique quantique, ainsi que les modèles d'autres phénomènes physiques, peuvent être formalisés de la même manière en termes d'EDP, dont la nature distribuée introduit un niveau supplémentaire de complexité. C'est pourquoi le contrôle et l'estimation des EDP sont aujourd'hui une direction de recherche très populaire, Barje et al, 2013.

. Bredies, , 2004.

. Krstic, , 2003.

K. Smyshlyaev, Vande Wouver and Zeitz, 2002, ensuite, le problème d'observation est abordé avec les outils bien connus disponibles pour les systèmes de dimension finie, tandis que l'évaluation de la convergence doit être effectuée par rapport aux solutions du système distribué d'origine. L'analyse et la conception dans les coordonnées distribuées d'origine sont plus compliquées, Dochain, 1982.