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Estimation de l'état des systèmes non linéaires à temps discret : Application à une station d'épuration

Abstract : This subject of research holds, on the one hand, a theoretical character since it tackles the state estimation problem for linear and nonlinear singular discrete time systems for which very few results are available and, on the other hand, a practical aspect because the used model is an activated sludge process for wastewater treatment. In the theoretical part, we were interested firstly in the state estimation problem of linear singular systems using the moving horizon approach. We have presented two optimal estimators with the least squares and the minimum variance formulations. The analysis of the convergence and the stability of the estimators are derived. Then, an observers synthesis method for nonlinear Lipschitz discrete-time systems is proposed. By supposing that the linear part of this class of systems is time-varying, the state estimation problem of nonlinear system is transformed into a state estimation problem for LPV system. The stability condition of the proposed observer is derived in the form of linear matrix inequalities (LMIs). Finally, in the practical part, the obtained results are validated by an application to an activated sludge process for wastewater treatment.
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Boulaïd Boulkroune. Estimation de l'état des systèmes non linéaires à temps discret : Application à une station d'épuration. Autre. Université Henri Poincaré - Nancy 1, 2008. Français. ⟨NNT : 2008NAN10136⟩. ⟨tel-01748455⟩

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