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Méthodes ensemblistes pour l'estimation d'état et de paramètres

Abstract : This work is dedicated to the development and the application of set-membership methods for state and parameter estimation for non-linear systems. Two classes of models are investigated: models given by closedforms expressions of complex variables and models described by ordinary differential equations (ODE). For models described by closed-forms expressions, parameter identification is achieved by set inversion techniques through interval analysis. Furthermore, a complex interval arithmetics using polar forms is developed where multiplication and division operations are exact but no longer addition and subtraction. Thus, in order to ensure minimality property, new algorithms based on analytical constrained optimization are given. This new polar interval arithmetic toolbox is associated with set inversion and used for parameter estimation in the bounded error context, for the dielectric and thermal analyses of materials. The second part of this work deals with set membership state and parameter estimation for non-linear systems described by ODEs. A new state estimator based on a predictor/corrector approach similar to the Kalman filtering, is given. This estimator relies on guaranteed numerical integration techniques and set inversion. Furthermore, a moving horizon state estimator is proposed. Finally, a parameter estimation technique is suggested for systems described by ODEs.
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Contributor : Tarek Raïssi <>
Submitted on : Tuesday, July 1, 2008 - 12:36:23 PM
Last modification on : Saturday, January 18, 2020 - 10:40:15 AM
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  • HAL Id : tel-00292380, version 1


Tarek Raïssi. Méthodes ensemblistes pour l'estimation d'état et de paramètres. Automatique / Robotique. Université Paris XII Val de Marne, 2004. Français. ⟨tel-00292380⟩



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