Feedback stabilization of non-uniform spatial pattern in reaction-diffusion systems

Author

Kashima, Kenji ; Ogawa, Tomomi ; Sakurai, Takayasu

Author_Institution

Grad. Sch. of Eng. Sci., Osaka Univ., Toyonaka, Japan

fYear

2013

fDate

17-19 June 2013

Firstpage

3759

Lastpage

3764

Abstract

In this paper, we formulate and solve feedback stabilization problem of unstable non-uniform spatial pattern in reaction-diffusion systems. By considering spatial spectrum dynamics, we obtain a finite dimensional approximation that takes over the semi-passivity of the original partial differential equation. By virtue of this property, we can show the diffusive coupling in the spatial frequency domain achieves the desired pattern formation.

Keywords

approximation theory; feedback; frequency-domain analysis; partial differential equations; pattern formation; reaction-diffusion systems; stability; diffusive coupling; feedback stabilization problem; finite dimensional approximation; partial differential equation; pattern formation; reaction-diffusion systems; semipassivity; spatial frequency domain; spatial spectrum dynamics; unstable nonuniform spatial pattern; Approximation methods; Couplings; Educational institutions; Feedback control; Partial differential equations; Pattern formation; Time factors;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference (ACC), 2013

Conference_Location

Washington, DC

ISSN

0743-1619

Print_ISBN

978-1-4799-0177-7

Type

conf

DOI

10.1109/ACC.2013.6580412

Filename

6580412