The aim of this paper is to study the boundary feedback stabilization of a two dimensional Burgers type equation with a Dirichlet boundary control and boundary measurements. Thus we have to deal with highly unbounded control and observation operators. We study the well posedness of the infinite dimensional system obtained by coupling a linear estimator with a linear feedback control law for the corresponding linearized parabolic system in a neighborhood of an unstable stationary solution. We prove the local stabilization of the system obtained by applying to the nonlinear equation the linear feedback control coupled with the linear compensator. Numerical experiments confirm the theoretical results.
DOI : 10.1051/cocv/2014037
Mots clés : Burgers equation, feedback law, estimation, boundary control, compensator, boundary measurements, semilinear parabolic equations
@article{COCV_2015__21_2_535_0, author = {Buchot, Jean-Marie and Raymond, Jean-Pierre and Tiago, Jorge}, title = {Coupling estimation and control for a two dimensional {Burgers} type equation}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {535--560}, publisher = {EDP-Sciences}, volume = {21}, number = {2}, year = {2015}, doi = {10.1051/cocv/2014037}, zbl = {1311.93032}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv/2014037/} }
TY - JOUR AU - Buchot, Jean-Marie AU - Raymond, Jean-Pierre AU - Tiago, Jorge TI - Coupling estimation and control for a two dimensional Burgers type equation JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2015 SP - 535 EP - 560 VL - 21 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2014037/ DO - 10.1051/cocv/2014037 LA - en ID - COCV_2015__21_2_535_0 ER -
%0 Journal Article %A Buchot, Jean-Marie %A Raymond, Jean-Pierre %A Tiago, Jorge %T Coupling estimation and control for a two dimensional Burgers type equation %J ESAIM: Control, Optimisation and Calculus of Variations %D 2015 %P 535-560 %V 21 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2014037/ %R 10.1051/cocv/2014037 %G en %F COCV_2015__21_2_535_0
Buchot, Jean-Marie; Raymond, Jean-Pierre; Tiago, Jorge. Coupling estimation and control for a two dimensional Burgers type equation. ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 2, pp. 535-560. doi : 10.1051/cocv/2014037. http://www.numdam.org/articles/10.1051/cocv/2014037/
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