# 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

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topThevenet, 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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