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Controlled Lagrangians and the stabilization of Euler-Poincaré mechanical systems

Bloch, Anthony M. and Leonard, Naomi Ehrich and Marsden, Jerrold E. (2001) Controlled Lagrangians and the stabilization of Euler-Poincaré mechanical systems. International Journal of Robust and Nonlinear Control, 11 (3). pp. 191-214. ISSN 1049-8923. doi:10.1002/rnc.572.

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In this paper we develop a constructive approach to the determination of stabilizing control laws for a class of Lagrangian mechanical systems with symmetry systems whose underlying dynamics are governed by the Euler-Poincaré equations. This work extends our previous work on the stabilization of mechanical control systems using the method of controlled Lagrangians. The guiding principle behind our methodology is to develop a class of stabilizing feedback control laws which yield closed-loop dynamics that remain in Lagrangian form. Using the methodology for Euler-Poincaré systems, we analyse stabilization of a satellite and an underwater vehicle controlled with momentum wheels.

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Additional Information:© 2001 John Wiley & Sons, Ltd. We thank John Baillieul, Francesco Bullo, Joel Burdick, Dong Eui Chang, P.S. Krishnaprasad, Richard Murray, Tudor Ratiu, Gloria Sanchez de Alvarez and Craig Woolsey for helpful comments. AMB would like to acknowledge partial research support by the National Science Foundation grant DMS-9803181 and AFOSR grant F49620-96-1-0100, NEL acknowledges partial support from the National Science Foundation under grant BES-9502477 and by the Office of Naval Research under grant N00014-98-1-0649 and JEM acknowledges partial support from the California Institute of Technology and AFOSR Grant F49620-95-1-0419.
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)F49620-96-1-0100
Office of Naval ResearchN00014-98-1-0649
California Institute of TechnologyUNSPECIFIED
Air Force Office of Scientific Research (AFOSR)F49620-95-1-0419
Subject Keywords:nonlinear control; stabilization; lagrangian systems; symmetry
Issue or Number:3
Record Number:CaltechAUTHORS:20100714-114021382
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19044
Deposited By: Ruth Sustaita
Deposited On:04 Aug 2010 17:34
Last Modified:08 Nov 2021 23:49

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