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Theses

(In-)validation de modèles de systèmes incertains

Abstract : The work presented in this dissertation deals with the theoretical analysis of the frequency domain model validation for uncertain systems which considers that the gap between the actual system and the nominal model results not only from disturbing noise but also from model uncertainty. By assuming that both of uncertainty and additive noise are norm bounded we defined the notion of the model-set. Those which we considered are described by a fractional linear representation. The generic question of model validation problem studied in this thesis is as follows: given experimental measurements and a model-set, does a model exist in the model-set which could produce the observed inputs/outputs data? It is simply required to find an element of models-set and an element of unknown of input signal set such that the information observed is produced exactly.
The problem of finding such a member of a model-set was formulated according to two strategies. First a noise signal of minimal norm is determined such that the data observed are generated by the model with an uncertainty of norm less than 1. The disadvantage of this method is that the optimization problem posed can be solved by LMI formalism only for special cases of model-set. The second strategy studied is to determine simultaneously the smallest norm of uncertainty and the smallest norm of the noise such that the model obtained generates the data observed. We have make a comparative study of these two problems and we have showed that the solution given with the help of generalized structured singular value not only makes it possible to answer the generic question for a more general class of the models-sets but also to take into account the structured nature of the uncertainty block.
The experimental process of 3Tanks as well as an academic example of simulation provided an excellent validation of the studied methods.
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Submitted on : Monday, February 13, 2006 - 4:18:53 PM
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Omar Mouhib. (In-)validation de modèles de systèmes incertains. Automatique / Robotique. Université Paris Sud - Paris XI, 2004. Français. ⟨tel-00011597⟩

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