Parallels between control PDEs and systems of ODEs

Author

Hunt, L.R. ; Villarreal, Ramiro

Author_Institution

Texas Univ., Dallas, Richardson, TX, USA

fYear

1988

fDate

7-9 Dec 1988

Firstpage

1269

Abstract

The authors introduce a particular linear partial differential equation (PDE) (called a Kolmogorov equation) that relates to the PDE as the linear system relates to the ODE (ordinary differential equation). For this particular PDE they introduce an appropriate feedback that allows eigenvalue placement if the equation is hypoelliptic. The authors study the effect of this feedback on the spatial Fourier transform of the solution. They also mention the problem of transforming (by state coordinate changes and feedback) the linear PDE to a Kolmogorov equation as one would transform the nonlinear system to a controllable linear system

Keywords

Fourier transforms; differential equations; distributed parameter systems; feedback; Kolmogorov equation; ODEs; control PDEs; distributed parameter systems; eigenvalue placement; feedback; linear partial differential equation; linear system; ordinary differential equation; spatial Fourier transform; Control systems; Differential equations; Eigenvalues and eigenfunctions; Fourier transforms; Linear feedback control systems; Linear systems; Nonlinear equations; Nonlinear systems; Partial differential equations; State feedback;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1988., Proceedings of the 27th IEEE Conference on

Conference_Location

Austin, TX

Type

conf

DOI

10.1109/CDC.1988.194526

Filename

194526