Controllability of Lie-Poisson reduced dynamics

Author

Manikonda, Vikram ; Krishnaprasad, P.S.

Author_Institution

Dept. of Electr. Eng., Maryland Univ., College Park, MD, USA

Volume

3

fYear

1997

fDate

4-6 Jun 1997

Firstpage

2203

Abstract

We present sufficient conditions for the controllability of the reduced dynamics of a class of mechanical systems with symmetry. We prove conditions (boundedness of coadjoint orbits and existence of a radially unbounded Lyapunov function) under which the drift vector field (of the reduced system) is weakly positively Poisson stable (WPPS). The WPPS nature of the drift vector field along with the Lie algebra rank condition is used to show controllability of the reduced system. We discuss the dynamics, Lie-Poisson reduction, and controllability of hovercraft and underwater vehicles, all treated as rigid bodies

Keywords

Lie algebras; controllability; dynamics; hovercraft; marine systems; nonlinear control systems; reduced order systems; space vehicles; stability; Lie algebra rank condition; Lie-Poisson reduced dynamics; drift vector field; hovercraft; mechanical systems; radially unbounded Lyapunov function; rigid bodies; sufficient conditions; symmetry; underwater vehicles; weakly positively Poisson stability; Algebra; Controllability; Educational institutions; Lagrangian functions; Lyapunov method; Mechanical systems; Orbits; Sufficient conditions; Underwater vehicles; Vehicle dynamics;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference, 1997. Proceedings of the 1997

Conference_Location

Albuquerque, NM

ISSN

0743-1619

Print_ISBN

0-7803-3832-4

Type

conf

DOI

10.1109/ACC.1997.611084

Filename

611084