Control of the Hopf bifurcation in the Takens-Bogdanov bifurcation

Author

Navarro, Francisco Armando Carrillo ; Gonzalez, áFernando Verduzco

Author_Institution

Math. Dept., Sonora Univ., Hermosillo, Mexico

fYear

2008

fDate

9-11 Dec. 2008

Firstpage

4438

Lastpage

4443

Abstract

It is a well-known result that in a versal deformation of the Takens-Bogdanov bifurcation is possible to find dynamical systems that undergo saddle-node, homoclinic and Hopf bifurcations. In this document a nonlinear control system in the plane is considered, whose nominal vector field undergoes the Takens-Bogdanov bifurcation, and then the idea is to design a scalar control law such that the closed-loop system undergoes the called controllable Hopf bifurcation.

Keywords

bifurcation; closed loop systems; control system synthesis; nonlinear control systems; nonlinear dynamical systems; Hopf bifurcation control; Takens-Bogdanov bifurcation; closed-loop system; dynamical system; homoclinic bifurcation; nominal vector field; nonlinear control system; saddle-node bifurcation; scalar control law design; Bifurcation; Control systems; Eigenvalues and eigenfunctions; Feedback; Hydrogen; Limit-cycles; Nonlinear control systems; Open loop systems; Stability; Stationary state; Central Manifold Theory; Hopf bifurcation; Normal Forms Theory; Takens-Bogdanov bifurcation; versal deformation;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2008. CDC 2008. 47th IEEE Conference on

Conference_Location

Cancun

ISSN

0191-2216

Print_ISBN

978-1-4244-3123-6

Electronic_ISBN

0191-2216

Type

conf

DOI

10.1109/CDC.2008.4739082

Filename

4739082