Contribution à la synthèse d'observateurs pour les systèmes non linéaires

Abstract : The aim of this thesis is the study and the development of observation techniques for nonlinear dynamical systems. After recalling some basic definitions of stability and observability of dynamical systems and giving a survey of the available state estimation techniques, we are interested in the problem of extended Kalman-type estimators design for nonlinear discrete-time systems. In this context, we have proposed and studied the convergence of severeal algorithms : convergence analysis of the classical extended Kalman filter in a determininistic context, design and convergence analysis of reduced-order extended Kalman-type observers (EKO), design and convergence analysis of an EKC for singular nonlinear systems and, finally, design and convergence analysis of a separate-bias EKO. The proposed algorithmq are reliable, straightforward to implement and applicable to large classes of nonlinear systems. The stability analysis of each of them is based on a new "exact" first oreder linearisation technique of the system. By the aid of this parametrisation, sufficient conditions to ensure convergence of the algorithms are established, and the connexions between the choice of some arbitrary weighting matrices and the performances improvement of the estimators are pointed out. the validity an applicability of our approach have been shown, firstly trough numerical simulations on a nonlinear identification problem, secondly through state estimation problems of physical processes like induction motors, bioprocesses or the bearings-only estimation problem, and finally, with real data through a combined stares and parameters estimation problem of an experimental SCARA robot.
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Didier Aubry. Contribution à la synthèse d'observateurs pour les systèmes non linéaires. Autre. Université Henri Poincaré - Nancy 1, 1999. Français. ⟨NNT : 1999NAN10049⟩. ⟨tel-01754358⟩

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