Fredholm transformation on Laplacian and rapid stabilization for the heat equations
| Autor: | Ludovick Gagnon, Amaury Hayat, Shengquan Xiang, Christophe Zhang |
|---|---|
| Přispěvatelé: | Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), École des Ponts ParisTech (ENPC), Département de Mathématiques - EPFL, Ecole Polytechnique Fédérale de Lausanne (EPFL), Ludovick Gagnon was partially supported by the French Grant ANR ODISSE (ANR-19-CE48-0004-01) and the French Grant ANR TRECOS (ANR-20-CE40-0009)., Amaury Hayat was financially supported by Ecole des Ponts Paristech., Shengquan Xiang was financially supported by the Chair of Partial Differential Equations at EPFL., Christophe Zhang was partially funded by the Chair Dynamics Control and Numerics (Alexander von Humboldt Professorship) of the Department of Data Science of the Friedrich Alexander Universität Erlangen-Nürnberg, and by the INRIA Grand-Est, ANR-19-CE48-0004,ODISSE,Synthèse d'observateur pour des systèmes de dimension infinie(2019), ANR-20-CE40-0009,TRECOS,Nouvelles directions en contrôle et stabilisation: Contraintes et termes non-locaux(2020) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
boundary control
backstepping rapid stabilization parabolic equations stabilizability feedback stabilization space controllability Fredholm transformation null controllability 2020 MSC: 93C20 93B17 93D15 93D23 Mathematics - Analysis of PDEs dimension Optimization and Control (math.OC) time stabilization FOS: Mathematics systems [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] Mathematics - Optimization and Control Analysis Analysis of PDEs (math.AP) |
| Popis: | We study the rapid stabilization of the heat equation on the 1-dimensional torus using the backstepping method with a Fredholm transformation. We prove that, under some assumption on the control operator, two scalar controls are necessary and sufficient to get controllability and rapid stabilization. This classical framework allows us to present the backstepping method with Fredholm transformations on Laplace operators in a sharp functional setting, which is the main objective of this work. Finally, we prove that the same Fredholm transformation also leads to the local rapid stability of the viscous Burgers equation. Comment: 57 pages |
| Databáze: | OpenAIRE |
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