Unbounded observation and boundary control problems for Burgers equation

Author

Kang, Sungkwon ; Ito, Kazufumi ; Burns, John A.

Author_Institution

Dept. of Math., Univ. of Southern California, Los Angeles, CA, USA

fYear

1991

fDate

11-13 Dec 1991

Firstpage

2687

Abstract

The Burgers equation is a simple one-dimensional model for convection diffusion phenomena. Due to the nonlinear nature of the convection, the solution of the Burgers equation produces steep gradients. Stabilization of these steep gradients by an unbounded observation and a boundary control is considered. Feedback control laws for both cases are constructed by using linearization. These linear feedback laws produce a desired degree of stability of the closed-loop nonlinear system on a certain energy space. The effects of the control law on relaxation of steep gradients are analyzed. A numerical algorithm for computing the feedback law is developed, and several numerical experiments were performed to validate the theoretical results

Keywords

closed loop systems; distributed parameter systems; feedback; linearisation techniques; nonlinear control systems; stability; Burgers equation; boundary control; convection; convection diffusion; distributed parameter systems; feedback; linearization; relaxation; stability; steep gradients; unbounded observation; Boundary conditions; Distributed parameter systems; Feedback control; Hilbert space; Mathematics; Nonlinear equations; Nonlinear systems; Regulators; Shock waves; Stability;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1991., Proceedings of the 30th IEEE Conference on

Conference_Location

Brighton

Print_ISBN

0-7803-0450-0

Type

conf

DOI

10.1109/CDC.1991.261841

Filename

261841