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. https://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:

URL	URL Type	Description
http://dx.doi.org/10.1109/CDC.2006.376695	DOI	UNSPECIFIED
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4177277	Publisher	UNSPECIFIED
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4177277&isnumber=4176993	Publisher	UNSPECIFIED
http://www.cds.caltech.edu/~marsden/bib/2006/17-BlLeMaZe2006/	Author	UNSPECIFIED

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 Agency	Grant Number
NSF	DMS-0305837
NSF	DMS-0604307
NSF	CMS-0408542
NSF	DMS-0504747
University of Michigan Rackham faculty grant	UNSPECIFIED
Air Force Office of Scientific Research (AFOSR)	FA9550-05-1-0343
NSF	DMS-0306017
NSF	DMS-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

Series Name:

IEEE Conference on Decision and Control

Record Number:

CaltechAUTHORS:20101008-090656626

Persistent URL:

https://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

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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:

03 Oct 2019 02:08

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