Stabilization of a coupled PDE-ODE system by boundary control

Author

Tang, Shuxia ; Xie, Chengkang

Author_Institution

Sch. of Math. & Syst. Sci., Southwest Univ., Chongqing, China

fYear

2010

fDate

15-17 Dec. 2010

Firstpage

4042

Lastpage

4047

Abstract

A coupled system of an ODE and a diffusion PDE is considered in this paper. Special techniques as well as the method of PDE backstepping are employed to construct controllers. Through transforming the system into an exponentially stable PDE-ODE cascade, a state feedback boundary controller is established. Moreover, an observer for anti-collocated setup is proposed, and the observer error is shown to exponentially converge to zero, then an output feedback boundary controller is obtained. For a scalar coupled PDE-ODE system, the boundary controller and observer, as well as the solution of the closed-loop system are given explicitly.

Keywords

closed loop systems; observers; partial differential equations; stability; state feedback; PDE backstepping; boundary control; closed loop system; coupled PDE ODE system; diffusion PDE; observer; stabilization; stable PDE ODE cascade; state feedback boundary controller; Backstepping; Equations; Heating; Mathematical model; Observers; Output feedback; State feedback; Boundary control; Coupled PDE-ODE system; Output feedback;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control (CDC), 2010 49th IEEE Conference on

Conference_Location

Atlanta, GA

ISSN

0743-1546

Print_ISBN

978-1-4244-7745-6

Type

conf

DOI

10.1109/CDC.2010.5718141

Filename

5718141