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Potential shaping and the method of controlled Lagrangians

Bloch, Anthony M. and Leonard, Naomi Ehrich and Marsden, J. J. (1999) Potential shaping and the method of controlled Lagrangians. In: Proceedings of the 38th IEEE Conference on Decision and Control, 1999. Vol.2. Institute of Electrical and Electronics Engineers , Piscataway, NJ, pp. 1652-1657. ISBN 0-7803-5250-5 http://resolver.caltech.edu/CaltechAUTHORS:BLOieeecdc99

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Abstract

We extend the method of controlled Lagrangians to include potential shaping for complete state-space stabilization of mechanical systems. The method of controlled Lagrangians 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.


Item Type:Book Section
Additional Information:“© 1999 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.” Research partially supported by the National Science Foundation grant DMS-9803181 and AFOSR grant F49620-96-1-0100. Research partially supported by the National Science Foundation under grant BES-9502477 and by the Office of Naval Research under grant N00014-98-1-0649. Research partially supported by AFOSR Grant F49620-95-1-0419.
Record Number:CaltechAUTHORS:BLOieeecdc99
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:BLOieeecdc99
Alternative URL:http://dx.doi.org/10.1109/CDC.1999.830261
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:538
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:14 Jul 2005
Last Modified:26 Dec 2012 08:40

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