Turbulent behavior for a boundary controlled Burgers´ equation

Author

Gilliam, D.S. ; Lee, D. ; Martin, C.F. ; Shubov, V.I.

Author_Institution

Dept. of Math., Texas Tech. Univ., Lubbock, TX, USA

Volume

1

fYear

1994

Firstpage

311

Abstract

We present certain results concerning the effect of boundary control on the structure of attractors for a boundary controlled viscous Burgers´ equation. The zero dynamics possesses a single global asymptotically stable equilibrium for all positive values of viscosity. In contrast the main result of this paper is that for a special class of disturbances there is a critical range of values of the closed loop system gains for which there exist multiple stationary solutions. In keeping with common terminology, this bifurcation of a single global equilibrium of the zero dynamics is referred to as turbulent behavior

Keywords

asymptotic stability; bifurcation; boundary layer turbulence; closed loop systems; feedback; flow control; viscosity; attractors; bifurcation; boundary control; closed loop system; global asymptotically stable equilibrium; turbulent behavior; viscosity; viscous Burgers´ equation; zero dynamics possesses; Bifurcation; Boundary conditions; Closed loop systems; Feedback loop; Mathematics; Navier-Stokes equations; Nonlinear dynamical systems; Open loop systems; Terminology; Viscosity;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1994., Proceedings of the 33rd IEEE Conference on

Conference_Location

Lake Buena Vista, FL

Print_ISBN

0-7803-1968-0

Type

conf

DOI

10.1109/CDC.1994.410911

Filename

410911