Back to Search Start Over

Exponential boundary feedback stabilization of a shock steady state for the inviscid Burgers equation

Authors :
Jean-Michel Coron
Amaury Hayat
Georges Bastin
Peipei Shang
UCL - SST/ICTM/INMA - Pôle en ingénierie mathématique
Centre for Systems Engineering and Applied Mechanics (CSAM)
Université Catholique de Louvain = Catholic University of Louvain (UCL)
Département de Mathématiques-Université de Paris XI
Université Paris-Sud - Paris 11 (UP11)
Control And GEometry (CaGE )
Inria de Paris
Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598))
Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)
Laboratoire Jacques-Louis Lions (LJLL (UMR_7598))
Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)
School of Mathematical Sciences [Shanghai]
Tongji University
Department of Mathematics [ETH Zurich] (D-MATH)
Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich] (ETH Zürich)
Laboratoire International Associé Sino-Français de Mathématiques Appliquées (LIASFMA)
French Corps des IPEF
ANR-15-CE23-0007,Finite4SoS,Commande et estimation en temps fini pour les Systèmes de Systèmes(2015)
Université Catholique de Louvain (UCL)
Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology in Zürich [Zürich] (ETH Zürich)
Source :
Mathematical Models and Methods in Applied Sciences, Vol. 29, no.02, p. 271-316 (2019), Mathematical Models and Methods in Applied Sciences, Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2019, 29 (2), pp.271-316. ⟨10.1142/S021820251950009X⟩, Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2019, 29 (2), pp.271-316, Mathematical Models and Methods in Applied Sciences, 2019, 29 (2), pp.271-316. ⟨10.1142/S021820251950009X⟩
Publication Year :
2019
Publisher :
World Scientific Pub Co Pte Lt, 2019.

Abstract

In this paper, we study the exponential stabilization of a shock steady state for the inviscid Burgers equation on a bounded interval. Our analysis relies on the construction of an explicit strict control Lyapunov function. We prove that by appropriately choosing the feedback boundary conditions, we can stabilize the state as well as the shock location to the desired steady state in [Formula: see text]-norm, with an arbitrary decay rate.

Details

ISSN :
17936314 and 02182025
Volume :
29
Database :
OpenAIRE
Journal :
Mathematical Models and Methods in Applied Sciences
Accession number :
edsair.doi.dedup.....1fc9d445b98076ccc4c450b32ba63964