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The equivalence of controlled Lagrangian and controlled Hamiltonian systems

Chang, Dong Eui and Bloch, Anthony M. and Leonard, Naomi E. and Marsden, Jerrold E. and Woolsey, Craig A. (2002) The equivalence of controlled Lagrangian and controlled Hamiltonian systems. ESAIM: Control, Optimisation and Calculus of Variations, 8 (Specia). pp. 393-422. ISSN 1262-3377. http://resolver.caltech.edu/CaltechAUTHORS:20100727-152201641

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Abstract

The purpose of this paper is to show that the method of controlled Lagrangians and its Hamiltonian counterpart (based on the notion of passivity) are equivalent under rather general hypotheses. We study the particular case of simple mechanical control systems (where the underlying Lagrangian is kinetic minus potential energy) subject to controls and external forces in some detail. The equivalence makes use of almost Poisson structures (Poisson brackets that may fail to satisfy the Jacobi identity) on the Hamiltonian side, which is the Hamiltonian counterpart of a class of gyroscopic forces on the Lagrangian side.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1051/cocv:2002045DOIUNSPECIFIED
http://www.esaim-cocv.org/index.php?option=com_article&access=standard&Itemid=129&url=/articles/cocv/abs/2002/02/Chang/Chang.htmlPublisherUNSPECIFIED
Additional Information:© EDP Sciences, SMAI 2002. Dedicated to the Memory of J.L. Lions. Received December 27, 2001. Revised February 26, 2002. We are grateful to the authors of [?] and of [?] for providing us advance copies of their papers and for helpful correspondence. Control and Dynamical Systems, California Institute of Technology, Pasadena, CA 91125; e-mail: dchang@cds.caltech.edu. Work partially supported by the California Institute of Technology and AFOSR grant ASOSR F49620-99-1-0190 Department of Mathematics, University of Michigan, Ann Arbor MI 48109; e-mail: abloch@math.lsa.umich.eduWork partially supported by NSF grants DMS 981283 and 0103895 and AFOSR Mechanical & Aerospace Engineering, Princeton University, Princeton, NJ 08544; e-mail: naomi@princeton.eduWork partially supported by NSF grant CCR-9980058, ONR grant N00014-98-1-0649 and AFOSR grant F49620-01-1-0382 Control and Dynamical Systems, California Institute of Technology, Pasadena, CA 91125; e-mail: marsden@cds.caltech.edu Work partially supported by the California Institute of Technology, NSF-KDI grant ATM-9873133 and AFOSR grant ASOSR F49620-99-1-0190. Aerospace & Ocean Engineering, Virginia Tech., Blacksburg, VA 24061, USA; e-mail: cwoolsey@vt.edu
Funders:
Funding AgencyGrant Number
California Institute of TechnologyUNSPECIFIED
Air Force Office of Scientific Research (AFOSR)ASOSR F49620-99-1-0190
NSFDMS 981283
NSF0103895
NSFCCR-9980058
Office of Naval Research (ONR)N00014-98-1-0649
Air Force Office of Scientific Research (AFOSR)F49620-01-1-0382
Subject Keywords:controlled Lagrangian, controlled Hamiltonian, energy shaping, Lyapunov stability, passivity, equivalence
Classification Code:AMS Subject Classification. 34D20,70H03,70H05,93D15
Record Number:CaltechAUTHORS:20100727-152201641
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20100727-152201641
Official Citation:Chang, D., et al. "The equivalence of controlled Lagrangian and controlled Hamiltonian systems." ESAIM. Control, optimisation and calculus of variations 8(2002):393-422.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19203
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:29 Jul 2010 23:29
Last Modified:26 Dec 2012 12:16

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