Published June 2002
| Version Accepted Version
Journal Article
Open
The equivalence of controlled Lagrangian and controlled Hamiltonian systems
Creators
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1.
California Institute of Technology
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2.
University of Michigan–Ann Arbor
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3.
Princeton University
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4.
Virginia Tech
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.
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.eduAttached Files
Accepted Version - ChBlLeMaWo2002.pdf
Files
ChBlLeMaWo2002.pdf
Additional details
Identifiers
- Eprint ID
- 19203
- Resolver ID
- CaltechAUTHORS:20100727-152201641
Funding
- California Institute of Technology
- Air Force Office of Scientific Research (AFOSR)
- ASOSR F49620-99-1-0190
- NSF
- DMS 981283
- NSF
- 0103895
- NSF
- CCR-9980058
- Office of Naval Research (ONR)
- N00014-98-1-0649
- Air Force Office of Scientific Research (AFOSR)
- F49620-01-1-0382
Dates
- Created
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2010-07-29Created from EPrint's datestamp field
- Updated
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2021-11-08Created from EPrint's last_modified field