Nonlinear feedback stabilization of a two-dimensional Burgers equation

Laetitia Thevenet; Jean-Marie Buchot; Jean-Pierre Raymond

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 16, Issue: 4, page 929-955
  • ISSN: 1292-8119

Abstract

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In this paper, we study the stabilization of a two-dimensional Burgers equation around a stationary solution by a nonlinear feedback boundary control. We are interested in Dirichlet and Neumann boundary controls. In the literature, it has already been shown that a linear control law, determined by stabilizing the linearized equation, locally stabilizes the two-dimensional Burgers equation. In this paper, we define a nonlinear control law which also provides a local exponential stabilization of the two-dimensional Burgers equation. We end this paper with a few numerical simulations, comparing the performance of the nonlinear law with the linear one.

How to cite

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Thevenet, Laetitia, Buchot, Jean-Marie, and Raymond, Jean-Pierre. "Nonlinear feedback stabilization of a two-dimensional Burgers equation." ESAIM: Control, Optimisation and Calculus of Variations 16.4 (2010): 929-955. <http://eudml.org/doc/250705>.

@article{Thevenet2010,
abstract = { In this paper, we study the stabilization of a two-dimensional Burgers equation around a stationary solution by a nonlinear feedback boundary control. We are interested in Dirichlet and Neumann boundary controls. In the literature, it has already been shown that a linear control law, determined by stabilizing the linearized equation, locally stabilizes the two-dimensional Burgers equation. In this paper, we define a nonlinear control law which also provides a local exponential stabilization of the two-dimensional Burgers equation. We end this paper with a few numerical simulations, comparing the performance of the nonlinear law with the linear one. },
author = {Thevenet, Laetitia, Buchot, Jean-Marie, Raymond, Jean-Pierre},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Dirichlet control; Neumann control; feedback control; stabilization; Burgers equation; Algebraic Riccati equation; algebraic Riccati equation},
language = {eng},
month = {10},
number = {4},
pages = {929-955},
publisher = {EDP Sciences},
title = {Nonlinear feedback stabilization of a two-dimensional Burgers equation},
url = {http://eudml.org/doc/250705},
volume = {16},
year = {2010},
}

TY - JOUR
AU - Thevenet, Laetitia
AU - Buchot, Jean-Marie
AU - Raymond, Jean-Pierre
TI - Nonlinear feedback stabilization of a two-dimensional Burgers equation
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/10//
PB - EDP Sciences
VL - 16
IS - 4
SP - 929
EP - 955
AB - In this paper, we study the stabilization of a two-dimensional Burgers equation around a stationary solution by a nonlinear feedback boundary control. We are interested in Dirichlet and Neumann boundary controls. In the literature, it has already been shown that a linear control law, determined by stabilizing the linearized equation, locally stabilizes the two-dimensional Burgers equation. In this paper, we define a nonlinear control law which also provides a local exponential stabilization of the two-dimensional Burgers equation. We end this paper with a few numerical simulations, comparing the performance of the nonlinear law with the linear one.
LA - eng
KW - Dirichlet control; Neumann control; feedback control; stabilization; Burgers equation; Algebraic Riccati equation; algebraic Riccati equation
UR - http://eudml.org/doc/250705
ER -

References

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