Controlled Lagrangians and the stabilization of mechanical systems. II. Potential shaping

Author

Bloch, Anthony M. ; Chang, Dong Eui ; Leonard, Naomi Ehrich ; Marsden, Jerrold E.

Author_Institution

Dept. of Math., Michigan Univ., Ann Arbor, MI, USA

Volume

46

Issue

10

fYear

2001

fDate

10/1/2001 12:00:00 AM

Firstpage

1556

Lastpage

1571

Abstract

For pt.I, see ibid., vol.45, p.2253-70 (2000). We extend the method of controlled Lagrangians (CL) to include potential shaping, which achieves complete state-space asymptotic stabilization of mechanical systems. The CL method deals with mechanical systems with symmetry and provides symmetry-preserving kinetic shaping and feedback-controlled dissipation for state-space stabilization in all but the symmetry variables. Potential shaping complements the kinetic shaping by breaking symmetry and stabilizing the remaining state variables. The approach also extends the method of controlled Lagrangians to include a class of mechanical systems without symmetry such as the inverted pendulum on a cart that travels along an incline

Keywords

Lyapunov methods; asymptotic stability; dynamics; nonlinear control systems; state-space methods; symmetry; controlled Lagrangians; feedback-controlled dissipation; inverted pendulum; mechanical systems; potential shaping; state-space asymptotic stabilization; symmetry-preserving kinetic shaping; Aerodynamics; Control systems; Equations; Kinetic theory; Lagrangian functions; Linear feedback control systems; Mechanical systems; Mechanical variables control; Nonlinear control systems; Shape control;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.956051

Filename

956051