Stabilization of Navier-Stokes equations by boundary feedback

被引：0

作者：

Ravindran, S. S. ^{[1
]}

机构：

[1] Univ Alabama, Dept Math Sci, Huntsville, AL 35899 USA

来源：

INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING | 2007年 / 4卷 / 3-4期

关键词：

Navier-Stokes equation; Riccati equation; stabilization; feedback control; linear quadratic regulator;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the stabilization of steady state solutions to Navier-Stokes equations by boundary feedback control. The feedback control is determined by solving a linear quadratic regulator problem associated with the linearized Navier-Stokes equations. The control is effected through suction and blowing at the boundary. We show that the linear feedback control provides global exponential stabilization of the steady state solutions to the Navier-Stokes equations for arbitrary Reynolds number. This feedback is shown to provide global stability in both L-2 and H-1-norms.

引用

页码：608 / 624

页数：17

共 23 条

[1]

Adams R., 1975, Sobolev Spaces

[2]

Anderson B.D., 2007, Optimal control

[3]

[Anonymous], S INT APPL AN FIZ MA

[4] H∞-control theory of fluid dynamics [J].

Barbu, V ;

Sritharan, SS .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1998, 454 (1979) :3009-3033

[5]

Bensoussan A., 1993, REPRESENTATION CONTR

[6] On the null asymptotic stabilization of the two-dimensional incompressible Euler equations in a simply connected domain [J].

Coron, JM .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1999, 37 (06) :1874-1896

[7] EXISTENCE OF OPTIMAL CONTROLS FOR VISCOUS-FLOW PROBLEMS [J].

FATTORINI, HO ;

SRITHARAN, SS .

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1992, 439 (1905) :81-102

[8]

GUNZBURGER MD, 1995, IMA, V68

[9] Numerical approximation of optimal flow control problems by a penalty method: Error estimates and numerical results [J].

Hou, LS ;

Ravindran, SS .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1999, 20 (05) :1753-1777

[10] A penalized Neumann control approach for solving an optimal Dirichlet control problem for the Navier-Stokes equations [J].

Hou, LS ;

Ravindran, SS .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1998, 36 (05) :1795-1814

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