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

Georges Bastin; Jean Michel Coron; Amaury Hayat; Peipei Shang

doi:10.1142/S021820251950009X

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

Georges Bastin
, Jean Michel Coron
, Amaury Hayat
, Peipei Shang

University of Louvain
UPMC Université de Paris VI
ETH Zurich
Tongji University

Research output: Contribution to journal › Article › peer-review

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 H2-norm, with an arbitrary decay rate.

Original language	English
Pages (from-to)	237-270
Number of pages	34
Journal	Mathematical Models and Methods in Applied Sciences
Volume	29
Issue number	2
DOIs	https://doi.org/10.1142/S021820251950009X
Publication status	Published - 1 Feb 2019
Externally published	Yes

Keywords

Burgers equation
boundary feedback controls
shock steady state

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10.1142/S021820251950009X

Cite this

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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 H2-norm, with an arbitrary decay rate.",

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AU - Coron, Jean Michel

AU - Hayat, Amaury

AU - Shang, Peipei

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Y1 - 2019/2/1

N2 - 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 H2-norm, with an arbitrary decay rate.

AB - 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 H2-norm, with an arbitrary decay rate.

KW - Burgers equation

KW - boundary feedback controls

KW - shock steady state

UR - https://www.scopus.com/pages/publications/85060188711

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DO - 10.1142/S021820251950009X

M3 - Article

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JO - Mathematical Models and Methods in Applied Sciences

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IS - 2

ER -

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

Abstract

Keywords

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