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Commande robuste de systèmes non linéaires incertains

Abstract : This work focuses on the LPV approach to control the nonlinear systems. The LPV (Linear Parameter Varying) has been proposed as an extension of the H ∞ approach in the context of systems depending on parameters varying in time or non-linear systems. More specifically, it was also shown that the LPV framework is a theoretical framework attractive and well placed to deal with control problems addressed by the engineers with the help of methods referring to the sequence of gains. However, the use of these approaches within the control of nonlinear systems is currently limited. Indeed, even beyond the theoretical limits (related to the intrinsic complexity of the robust control of nonlinear systems), it is the nature of the solutions obtained by these approaches does not seem adequate. This is a reason that motivated a big part in this thesis. We also show in this study, that the primary nature of the informational scheme used in the synthesis LPV which explains the low variation of markers found and that under reasonable assumptions, the LPV framework may even cover strategies such as "linearization closure ". This being the case, a second difficulty has been overcome: the problem of integrability of corrective ACL. Indeed, the solution of problems type gains variables leads to a synthesis in two steps: the first is the synthesis of an LPV on linearization correction (within the meaning of Cakes) of the nonlinear system and the second is the integration of the corrector LPV. Through the resolution of an LPV problem with a specific information structure (compatible with that identified in the first part), we propose for the first time a rigorous mathematical framework to effectively address the problem of incremental weighted synthesis. This study and its outcome to the definition of a formal framework and a complete procedure for obtaining markers, including methods to reduce complexity, provide powerful arguments in favor of an approach to a robust nonlinear control through the LPV approach.
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Contributor : Josiane Dartron <>
Submitted on : Thursday, November 17, 2011 - 2:52:23 PM
Last modification on : Thursday, March 29, 2018 - 11:06:05 AM
Document(s) archivé(s) le : Saturday, February 18, 2012 - 2:32:59 AM


  • HAL Id : tel-00642160, version 1


Safta de Hillerin. Commande robuste de systèmes non linéaires incertains. Automatique / Robotique. Supélec, 2011. Français. ⟨tel-00642160v1⟩



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