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Contribution à l’estimation robuste de modèles dynamiques : Application à la commande de systèmes dynamiques complexes.

Abstract : Complex dynamic systems identification remains a concern when prediction errors contain innovation outliers. They have the effect to damage the estimated model if the estimation criterion is badly chosen and badly adapted. The consequence is the contamination of the distribution of these errors; this distribution presents heavy tails and deviates of the normal distribution. To solve this problem, there is a robust estimator's class, less sensitive to the outliers, which treat the transition between residuals of very different levels in a softer way. The Huber's M-estimators belong to this class. They are associated to a mixed L2 - L1 norm, related to a disturbed Gaussian distribution model, namely gross error model. From this formal context, in this thesis we propose a set of estimation and validation tools of black-box linear and pseudo-linear models, with extension of the noise interval to low values of the tuning constant in the Huber's norm. We present the convergence properties of the robust estimation criterion and the robust estimator. We show that the extension of the noise interval reduces the sensitivity of the bias of the estimator and improves the robustness to the leverage points. Moreover, for a pseudo-linear model structure, we present a new context, named L-FTE, with a new method to determine L, in order to linearize the gradient and the Hessien of estimation criterion and the asymptotic covariance matrix of the estimator. From these expressions, a robust version of the FPE validation criterion is established and we propose a new decisional tool for the estimated model choice. Experiments on simulated and real systems are presented and analyzed.
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https://pastel.archives-ouvertes.fr/pastel-00832168
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Submitted on : Monday, June 10, 2013 - 11:40:10 AM
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  • HAL Id : pastel-00832168, version 1

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Christophe Corbier. Contribution à l’estimation robuste de modèles dynamiques : Application à la commande de systèmes dynamiques complexes.. Autre. Ecole nationale supérieure d'arts et métiers - ENSAM, 2012. Français. ⟨NNT : 2012ENAM0041⟩. ⟨pastel-00832168⟩

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