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Controlled Lagrangians and Potential Shaping for Stabilization of Discrete Mechanical Systems

Bloch, Anthony M. and Marsden, Jerrold E. and Leok, Melvin and Zenkov, Dmitry V. (2006) Controlled Lagrangians and Potential Shaping for Stabilization of Discrete Mechanical Systems. In: Proceedings of the 45th IEEE Conference on Decision and Control. IEEE Conference on Decision and Control . Piscataway, NJ , IEEE, pp. 3333-3338. ISBN 978-1-4244-0170-3 http://resolver.caltech.edu/CaltechAUTHORS:20101008-090656626

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Abstract

The method of controlled Lagrangians for discrete mechanical systems is extended to include potential shaping in order to achieve complete state-space asymptotic stabilization. New terms in the controlled shape equation that are necessary for matching in the discrete context are introduced. The theory is illustrated with the problem of stabilization of the cart-pendulum system on an incline. We also discuss digital and model predictive control.


Item Type:Book Section
Related URLs:
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http://dx.doi.org/10.1109/CDC.2006.376695 DOIUNSPECIFIED
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4177277PublisherUNSPECIFIED
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4177277&isnumber=4176993PublisherUNSPECIFIED
http://www.cds.caltech.edu/~marsden/bib/2006/17-BlLeMaZe2006/AuthorUNSPECIFIED
Additional Information:© 2006 IEEE. The authors would like to thank the reviewers for helpful remarks. The research of AMB was supported by NSF grants DMS-0305837, DMS-0604307, and CMS-0408542. The research of ML was partially supported by NSF grant DMS-0504747 and a University of Michigan Rackham faculty grant. The research of JEM was partially supported by AFOSR Contract FA9550-05-1-0343. The research of DVZ was partially supported by NSF grants DMS-0306017 and DMS-0604108.
Funders:
Funding AgencyGrant Number
NSFDMS-0305837
NSFDMS-0604307
NSFCMS-0408542
NSFDMS-0504747
University of Michigan Rackham faculty grantUNSPECIFIED
Air Force Office of Scientific Research (AFOSR)FA9550-05-1-0343
NSFDMS-0306017
NSFDMS-0604108
Subject Keywords:cart-pendulum system , controlled Lagrangians , controlled shape equation , digital control , discrete mechanical system , model predictive control , potential shaping , state-space asymptotic stabilization
Record Number:CaltechAUTHORS:20101008-090656626
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20101008-090656626
Official Citation:Bloch, A.M.; Marsden, J.E.; Leok, M.; Zenkov, D.V.; , "Controlled Lagrangians and Potential Shaping for Stabilization of Discrete Mechanical Systems," Decision and Control, 2006 45th IEEE Conference on , vol., no., pp.3333-3338, 13-15 Dec. 2006 doi: 10.1109/CDC.2006.376695
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20346
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:23 Nov 2010 00:30
Last Modified:26 Dec 2012 12:30

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