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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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|
|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.|
|Subject Keywords:||cart-pendulum system , controlled Lagrangians , controlled shape equation , digital control , discrete mechanical system , model predictive control , potential shaping , state-space asymptotic stabilization|
|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.|
|Deposited By:||Tony Diaz|
|Deposited On:||23 Nov 2010 00:30|
|Last Modified:||26 Dec 2012 12:30|
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