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Observateurs et commande basée observateur pour les systèmes bilinéaires

Abstract : The control and the estimation of the bilinear systems remain an unsolved problem in control theory because of the nonlinear nature of the systems. Even if these systems seem close to the linear systems, their study requires a different approach. Indeed, control input can generate singularities which must be explicitly taken into account in the synthesis of the control laws and the observers. Therefore the problem of the observation was treated following two main approaches : LPV approach ; approach based on the structural analysis of the bilinear systems. One of the contributions presented in this thesis is the use of the LPV approach taking into account the inputs of command in order to design an observer for the bilinear systems. The H8 approach for filtering of the disturbances was studied for two kinds of observers, the observer with high gain, especially adapted to the uniformly observable systems, and the functional observer. LMI approaches allow the synthesis and the optimization of these filters. So thanks to this approach, various saturated control laws based on these observers were proposed : bang bang control, quadratic control, linear control, coupled use of controls. Another part of this thesis focuses on exploiting the structure of the bilinear systems in order to reduce conservatism in the processing of the inputs in observer synthesis. A two-stage observer is designed in order to separate dynamics of the uniformly observable part and those of the non uniformly observable part, in order to apply various types of LPV observers to each part. Moreover this approach shows the possibilities of association of various types of observers for the large-scale systems.
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Benjamin Gérard. Observateurs et commande basée observateur pour les systèmes bilinéaires. Autre. Université Henri Poincaré - Nancy 1, 2008. Français. ⟨NNT : 2008NAN10108⟩. ⟨tel-01748484⟩



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