Geodesic
Nonlinear feedback stabilization of a two-dimensional Burgers equation
ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 4, pp. 929-955

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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.

DOI : 10.1051/cocv/2009028
Classification : 93B52, 93C20, 93D15
Keywords: Dirichlet control, Neumann control, feedback control, stabilization, Burgers equation, algebraic Riccati equation 
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     author = {Thevenet, Laetitia and Buchot, Jean-Marie and Raymond, Jean-Pierre},
     title = {Nonlinear feedback stabilization of a two-dimensional {Burgers} equation},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {929--955},
     publisher = {EDP-Sciences},
     volume = {16},
     number = {4},
     year = {2010},
     doi = {10.1051/cocv/2009028},
     mrnumber = {2744156},
     zbl = {1202.93129},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2009028/}
}
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Thevenet, Laetitia; Buchot, Jean-Marie; Raymond, Jean-Pierre. Nonlinear feedback stabilization of a two-dimensional Burgers equation. ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 4, pp. 929-955. doi: 10.1051/cocv/2009028

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