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Contribution à la commande non linéaire par des approches linéaires

Yann Labit 1
1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : The thesis is concerned with the control problem synthesis for nonlinear systems using linear techniques. The proposed approach consists on an approximation of the nonlinear system by a set of uncertain linear systems. Control laws of these models are designed using classical methods (LQ, LQG, pole placement, H2, H¥, etc). The global law is based on gain scheduling from the measured state of the system. There exists some multi-model approaches which work in this direction but they still have a high degree of imprecision and approximation. For the validation of these approaches, a lot of simulations are needed. The proposed approach defines a step by step control synthesis which exhibits a level of guaranteed performances. The first step is given by the approximation of the nonlinear system into a set of uncertain linear systems (piecewise linear model) with a defined level of precision. The second step is the use of robust control methods based on LMIs that assure local stability in a non-infinitesimal state space domain. This last point permits to tune the complexity of the global control law with the cardinality of the set of local linear systems. This approach is illustrated through several regulation problems: inverted pendulum, electrical motor and solar panel.
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Submitted on : Monday, February 19, 2007 - 1:55:59 PM
Last modification on : Monday, December 14, 2020 - 5:03:01 PM
Long-term archiving on: : Wednesday, April 7, 2010 - 12:12:52 AM


  • HAL Id : tel-00131792, version 1


Yann Labit. Contribution à la commande non linéaire par des approches linéaires. Mathématiques [math]. INSA de Toulouse, 2002. Français. ⟨tel-00131792⟩



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