Feedback stabilization of the 2-D and 3-D Navier-Stokes equations based on an extended system
ESAIM: Control, Optimisation and Calculus of Variations (2008)
- Volume: 15, Issue: 4, page 934-968
- ISSN: 1292-8119
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topBadra, Mehdi. "Feedback stabilization of the 2-D and 3-D Navier-Stokes equations based on an extended system." ESAIM: Control, Optimisation and Calculus of Variations 15.4 (2008): 934-968. <http://eudml.org/doc/90945>.
@article{Badra2008,
abstract = { We study the local exponential stabilization of the 2D and 3D
Navier-Stokes equations in a bounded domain, around a given
steady-state flow, by means of a boundary control. We look for a
control so that the solution to the Navier-Stokes equations be a
strong solution. In the 3D case, such solutions may exist if the
Dirichlet control satisfies a compatibility condition with the
initial condition. In order to determine a feedback law satisfying
such a compatibility condition, we consider an extended system
coupling the Navier-Stokes equations with an equation satisfied by
the control on the boundary of the domain. We determine a linear
feedback law by solving a linear quadratic control problem for the
linearized extended system. We show that this feedback law also
stabilizes the nonlinear extended system.
},
author = {Badra, Mehdi},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Navier-Stokes equation; feedback stabilization;
Dirichlet control; Riccati equation; Dirichlet control},
language = {eng},
month = {10},
number = {4},
pages = {934-968},
publisher = {EDP Sciences},
title = {Feedback stabilization of the 2-D and 3-D Navier-Stokes equations based on an extended system},
url = {http://eudml.org/doc/90945},
volume = {15},
year = {2008},
}
TY - JOUR
AU - Badra, Mehdi
TI - Feedback stabilization of the 2-D and 3-D Navier-Stokes equations based on an extended system
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2008/10//
PB - EDP Sciences
VL - 15
IS - 4
SP - 934
EP - 968
AB - We study the local exponential stabilization of the 2D and 3D
Navier-Stokes equations in a bounded domain, around a given
steady-state flow, by means of a boundary control. We look for a
control so that the solution to the Navier-Stokes equations be a
strong solution. In the 3D case, such solutions may exist if the
Dirichlet control satisfies a compatibility condition with the
initial condition. In order to determine a feedback law satisfying
such a compatibility condition, we consider an extended system
coupling the Navier-Stokes equations with an equation satisfied by
the control on the boundary of the domain. We determine a linear
feedback law by solving a linear quadratic control problem for the
linearized extended system. We show that this feedback law also
stabilizes the nonlinear extended system.
LA - eng
KW - Navier-Stokes equation; feedback stabilization;
Dirichlet control; Riccati equation; Dirichlet control
UR - http://eudml.org/doc/90945
ER -
References
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