Skip to Main content Skip to Navigation
Theses

EXTENSION DE LA NOTION DE PLATITUDE A DES SYSTEMES DECRITS PAR DES EQUATIONS AUX DERIVEES PARTIELLES LINEAIRES

Abstract : Flatness has been already well defined and widely studied for finite dimensional dynamical systems. One of the remarquable consequences of this property is to allow parametrization of trajectories (both state and control) by free functions and their derivatives. It therefore provides an easy solution to an important problem in control theory : motion planning. For linear finite dimensional systems, flatness is exactly equivalent to controllability, via the Brunovsky canonical decomposition. This work proposes a definition of flatness for a class of infinite dimensional systems and extends Brunovsky canonical decomposition to infinite dimension. Following this new definition, the problem of flatness for a general linear 1-D diffusion equation is completely studied. A method allowing the effective computation of flat trajectories is given, and the canonical nature of this representation of trajectories is proved. Other example are studied, including the linear Kortewerg De Vries 1-D equation and a 2-D diffusion equation, which shows that the method is applicable to a wide range of problems.
Document type :
Theses
Complete list of metadatas

Cited literature [57 references]  Display  Hide  Download

https://pastel.archives-ouvertes.fr/tel-00454012
Contributor : Béatrice Laroche <>
Submitted on : Sunday, February 7, 2010 - 1:15:43 PM
Last modification on : Wednesday, September 16, 2020 - 4:43:08 PM
Long-term archiving on: : Friday, June 18, 2010 - 7:18:51 PM

Identifiers

  • HAL Id : tel-00454012, version 1

Collections

Citation

Béatrice Laroche. EXTENSION DE LA NOTION DE PLATITUDE A DES SYSTEMES DECRITS PAR DES EQUATIONS AUX DERIVEES PARTIELLES LINEAIRES. Automatique / Robotique. École Nationale Supérieure des Mines de Paris, 2000. Français. ⟨tel-00454012⟩

Share

Metrics

Record views

948

Files downloads

683