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Habilitation à diriger des recherches

Commande des Systèmes Hyperboliques décrits par des Equations aux Dérivées Partielles

Abstract : This work is part, from a theoretical point of view, of the control of systems described by partial differential equations (PDE). The other aspect is the application of those results to real process’s applications. Great developments have been done on modelization technics, identification and the control for systems in finite dimension since a long time. Those technics have reached a maturity level, and are applied to numerous applications. Nevertheless, the development of advanced technologies have for consequence to increase the size of the controlled models, rising which is the symbol of the passage from finite dimension system to infinite dimension system. In recent decades, a real work on the development of infinite dimension tools has emerged. This work originally dedicated to rather academic cases are being extended today to practical cases. My work has found its place at this level : since 10 years I am interested in stability problems and in the development of controls for systems described by hyperbolic PDE. For this I use mathematical structures such as semigroups, "natural" invariants like the Riemann invariants, energy structures like the Hamiltonian functional, or by the extension of existing results in finite dimension to the infinite dimension such for the LMI (Linear Matrices Inequalities) to LOI (Linear Operator Inequalities). All these theoretical results have no interest if they are not applied, at least that’s the goal I would like to maintain. To this end, all results have been developed on real processes : irrigation channels, navigable waterways, extrusion process, and more to come. The issue of water described by the shallow water equations is a central example in my work, but this is simply because I have access to benchmarks allowing me to validate the developed approaches. All of my works has been published internationally, but also broadcasted on lessons from doctoral schools, in training of masters students and PhD students.
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Habilitation à diriger des recherches
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https://hal.inria.fr/tel-01241225
Contributor : Valérie dos Santos Martins <>
Submitted on : Thursday, December 10, 2015 - 10:52:37 AM
Last modification on : Friday, October 23, 2020 - 4:52:17 PM
Long-term archiving on: : Saturday, April 29, 2017 - 11:39:37 AM

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Valérie dos Santos Martins. Commande des Systèmes Hyperboliques décrits par des Equations aux Dérivées Partielles. Automatique / Robotique. Université de Lyon 1, 2015. ⟨tel-01241225⟩

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