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Theses

Identification de systèmes non linéaires blocs

Abstract : This thesis deals with the problem of identifying nonlinear systems based on bloc models. Two types of models are considered, those of Hammerstein and those of Wiener. Most of previous solutions have been designed under restrictive constraints regarding the nonlinear element of the model. This has been usually supposed to be smooth (or even polynomial), invertible and memoryless. In the case of Hammerstein systems, an identification scheme is designed that involves no assumptions on the nonlinear element except that it is memoryless and L/-stable. In ideal situations (undisturbed system), the proposed scheme determines exactly the parameters of the linear subsystem as well as a set of points of the nonlinear subsystem characteristic. This scheme is then adapted to the case where the structure of the nonlinear element is known. Then, the focus is particularly made on piecewise affine discontinuous nonlinearities. The part of this thesis that deals with Hammerstein systems identification is completed considering the problem of identifying systems that includes memory nonlinear elements. Two families of this type are focused on: the first one includes (unsaturated) hysteresis elements; the second one involves hysteresis-relay elements. The problem is coped with building up an identification scheme for which consistence results are achieved in presence of disturbances that can be assimilated to white noise that affects the output. The last part of this report is centred on the identification of Wiener systems whose nonlinear element is not necessarily invertible. Two identification schemes are constructed, to deal with this problem, and shown to be consistent in the same conditions as previously concerning the disturbances. The persistent excitation requirement plays a central role in the in this thesis. The different identification schemes are given this property through impulse type input signals. To this end, a technical lemma is developed that describes, in a general framework, how persistent excitation can be provided to linear systems. The exploitation of this lemma in the nonlinear context is illustrated through the analysis and design of the different identification schemes
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  • HAL Id : tel-00261896, version 1

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Youssef Rochdi. Identification de systèmes non linéaires blocs. Autre [cs.OH]. Université de Caen, 2006. Français. ⟨tel-00261896⟩

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