Title :
Controllability of Lie-Poisson reduced dynamics
Author :
Manikonda, Vikram ; Krishnaprasad, P.S.
Author_Institution :
Dept. of Electr. Eng., Maryland Univ., College Park, MD, USA
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;
Conference_Titel :
American Control Conference, 1997. Proceedings of the 1997
Conference_Location :
Albuquerque, NM
Print_ISBN :
0-7803-3832-4
DOI :
10.1109/ACC.1997.611084
