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Nonlinear feedback stabilizationof a two-dimensional Burgers equation

Published online by Cambridge University Press:  31 July 2009

Laetitia Thevenet ,
Jean-Marie Buchot  and
Jean-Pierre Raymond
Laetitia Thevenet
Affiliation:
Université de Toulouse, UPS, Institut de Mathématiques, UMR CNRS 5219, 31062 Toulouse Cedex 9, France. Laetitia.Thevenet@math.univ-toulouse.fr; jean-marie.buchot@math.univ-toulouse.fr; raymond@math.univ-toulouse.fr
Jean-Marie Buchot
Affiliation:
Université de Toulouse, UPS, Institut de Mathématiques, UMR CNRS 5219, 31062 Toulouse Cedex 9, France. Laetitia.Thevenet@math.univ-toulouse.fr; jean-marie.buchot@math.univ-toulouse.fr; raymond@math.univ-toulouse.fr
Jean-Pierre Raymond
Affiliation:
Université de Toulouse, UPS, Institut de Mathématiques, UMR CNRS 5219, 31062 Toulouse Cedex 9, France. Laetitia.Thevenet@math.univ-toulouse.fr; jean-marie.buchot@math.univ-toulouse.fr; raymond@math.univ-toulouse.fr
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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.

Keywords

Dirichlet controlNeumann controlfeedback controlstabilizationBurgers equationAlgebraic Riccati equation
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 16 , Issue 4 , October 2010 , pp. 929 - 955
Copyright
© EDP Sciences, SMAI, 2009

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