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Habilitation à diriger des recherches

Equivalence et Linearisation des systèmes de contrôle

Abstract :

Models of continuous-time finite-dimensional control systems are under-determined ordinary differential equations. This under-determination (only part of the time-derivatives are prescribed; some variables, the controls, are free) makes the class of transformations potentially very rich and the classification problem quite different from the one of dynamical systems (without control, determined ordinary differential equations). In chapter one (in French) (the only original part), an effort has been done in clarifying and unifying the different types of transformations (static, dynamic, functional..) by translating all of them in terms of correspondences between sets of solutions. Contributions in terms of geometric conditions are then presented, as well as open problems; all details are contained in eight published articles, reproduced in the following chapters (in English) with minor cross-referencing modifications.

Two main motivations for understanding better the structure of the set of models, equivalence and transformations are
- analyzing, understanding and possibly simplifying a model may considerably ease the design of a controller based on this model,
- choosing a model requires a deep understanding of the class of models, that is, to date, mostly missing (for instance: how do I know that two models translate "the same" reality?); nonlinear modeling or identification are still immature because of this lack of foundations.

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Habilitation à diriger des recherches
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Submitted on : Wednesday, November 4, 2009 - 4:00:12 PM
Last modification on : Monday, October 14, 2019 - 3:12:02 PM
Long-term archiving on: : Tuesday, October 16, 2012 - 1:15:42 PM

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Jean-Baptiste Pomet. Equivalence et Linearisation des systèmes de contrôle. Mathématiques [math]. Université Nice Sophia Antipolis, 2009. ⟨tel-00429825⟩

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