| Issue |
ESAIM: COCV
Volume 21, Number 2, April-June 2015
|
|
|---|---|---|
| Page(s) | 535 - 560 | |
| DOI | https://doi.org/10.1051/cocv/2014037 | |
| Published online | 09 March 2015 | |
Coupling estimation and control for a two dimensional Burgers type equation∗
1 Institut de Mathématiques de
Toulouse, UMR CNRS 5219, Université Paul Sabatier, 31062
Toulouse cedex 9,
France.
jean-marie.buchot@math.univ-toulouse.fr
2 Institut de Mathématiques de
Toulouse, UMR CNRS 5219, Université Paul Sabatier, 31062
Toulouse cedex 9,
France.
jean-pierre.raymond@math.univ-toulouse.fr
3 CEMAT-IST,
Lisbon,
Portugal.
jftiago@math.ist.utl.pt
Received:
12
June
2013
Revised:
26
June
2014
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.
Mathematics Subject Classification: 93B52 / 93C20 / 93E10
Key words: Burgers equation / feedback law / estimation / boundary control / compensator / boundary measurements / semilinear parabolic equations
© EDP Sciences, SMAI, 2015
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.