Poisson reduction via feedback invariant distributions

Author

Höffner, K. ; Guay, M.

fYear

2009

fDate

15-18 Dec. 2009

Firstpage

7466

Lastpage

7471

Abstract

The reduction of Poisson structures on the state space of controlled Hamiltonian system is studied. The existence of completely integrable feedback-invariant distributions gives rise to a collection of reduced Poisson structures on the quotient by maximal integrable submanifolds. In special cases we can define a Poisson subsystem, which is feedback invariant. The result is an initial step towards the development of a normal form for controlled Hamiltonian system based on the information contained of the accessibility algebra.

Keywords

Poisson distribution; algebra; feedback; state-space methods; Poisson reduction; Poisson structures reduction; Poisson subsystem; accessibility algebra; controlled Hamiltonian system; feedback invariant distribution; feedback-invariant distribution; maximal integrable submanifolds; reduced Poisson structures; state space; Algebra; Control systems; Damping; Mechanical systems; Nonlinear control systems; Poisson equations; Potential energy; Power system interconnection; State feedback; State-space methods;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on

Conference_Location

Shanghai

ISSN

0191-2216

Print_ISBN

978-1-4244-3871-6

Electronic_ISBN

0191-2216

Type

conf

DOI

10.1109/CDC.2009.5400337

Filename

5400337