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Controlled Lagrangians and Stabilization of the Discrete Cart-Pendulum System

Bloch, Anthony M. and Leok, Melvin and Marsden, Jerrold E. and Zenkov, Dmitry V. (2006) Controlled Lagrangians and Stabilization of the Discrete Cart-Pendulum System. In: 44th IEEE Conference on Decision and Control & European Control Conference. IEEE , Piscataway, NJ, pp. 6579-6584. ISBN 0-7803-9567-0 http://resolver.caltech.edu/CaltechAUTHORS:20101001-143905956

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Abstract

Matching techniques are developed for discrete mechanical systems with symmetry. We describe new phenomena that arise in the controlled Lagrangian approach for mechanical systems in the discrete context. In particular, one needs to either make an appropriate selection of momentum levels or introduce a new parameter into the controlled Lagrangian to complete the matching procedure. We also discuss digital and model predictive control.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/CDC.2005.1583218DOIUNSPECIFIED
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1583218PublisherUNSPECIFIED
Additional Information:© 2005 IEEE. The authors would like to thank the reviewers for helpful remarks. The research of AMB was supported by NSF grants DMS-0103895, DMS-030583, 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 ONR MURI Contract 00000916. The research of DVZ was partially supported by NSF grant DMS-0306017. AMB and DVZ would also like to thank the CRM, Barcelona, where part of this research was carried out.
Funders:
Funding AgencyGrant Number
NSFDMS-0103895
NSFDMS-030583
NSFCMS-0408542
NSFDMS-0504747
University of Michigan Rackham faculty grantUNSPECIFIED
Office of Naval Research (ONR)00000916
NSFDMS-0306017
Record Number:CaltechAUTHORS:20101001-143905956
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20101001-143905956
Official Citation:Bloch, A.M.; Leok, M.; Marsden, J.E.; Zenkov, D.V.; , "Controlled Lagrangians and Stabilization of the Discrete Cart-Pendulum System," Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC '05. 44th IEEE Conference on , vol., no., pp. 6579- 6584, 12-15 Dec. 2005 doi: 10.1109/CDC.2005.1583218 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1583218&isnumber=33412
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20254
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:01 Oct 2010 22:09
Last Modified:26 Dec 2012 12:29

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