Nonlinear boundary feedback control of the one-dimensional wave equation

Author

Chen, Goong ; Huang, Tingwen ; Hsu, Sze-Bi

Author_Institution

Dept. of Math., Texas A&M Univ., College Station, TX, USA

Volume

3

fYear

2000

fDate

2000

Firstpage

2060

Abstract

In this paper, we analyze the dynamical behavior of the linear wave equation on an interval, where the right endpoint has a van der Pol type nonlinearity or boundary controller, while the left endpoint has a boundary condition involving displacement. The asymptotic behavior of the system can be classified into two basic types: classical unbounded instability, or spatial pointwise convergence to periodic points of a nonlinear map corresponding to the van der Pol condition

Keywords

boundary-value problems; chaos; convergence; feedback; nonlinear control systems; wave equations; 1D wave equation; asymptotic behavior; boundary controller; displacement; dynamical behavior; left endpoint boundary condition; linear wave equation; nonlinear boundary feedback control; nonlinear map; periodic points; spatial pointwise convergence; unbounded instability; van der Pol type nonlinearity; Boundary conditions; Chaos; Feedback control; Force feedback; Instruments; Mathematics; Negative feedback; Partial differential equations; Pediatrics; Underwater acoustics;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2000. Proceedings of the 39th IEEE Conference on

Conference_Location

Sydney, NSW

ISSN

0191-2216

Print_ISBN

0-7803-6638-7

Type

conf

DOI

10.1109/CDC.2000.914097

Filename

914097