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Discrete mechanics and optimal control: An analysis

Ober-Blöbaum, Sina and Junge, Oliver and Marsden, Jerrold E. (2011) Discrete mechanics and optimal control: An analysis. ESAIM: Control, Optimisation and Calculus of Variations, 17 (2). pp. 322-352. ISSN 1292-8119.

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The optimal control of a mechanical system is of crucial importance in many application areas. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion sequences in robotics and biomechanics. In most cases, some sort of discretization of the original, infinite-dimensional optimization problem has to be performed in order to make the problem amenable to computations. The approach proposed in this paper is to directly discretize the variational description of the system's motion. The resulting optimization algorithm lets the discrete solution directly inherit characteristic structural properties from the continuous one like symmetries and integrals of the motion. We show that the DMOC (Discrete Mechanics and Optimal Control) approach is equivalent to a finite difference discretization of Hamilton's equations by a symplectic partitioned Runge-Kutta scheme and employ this fact in order to give a proof of convergence. The numerical performance of DMOC and its relationship to other existing optimal control methods are investigated.

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Additional Information:© 2010 EDP Sciences, SMAI. Received October 8, 2008. Revised September 17, 2009. Published online March 31, 2010. Published online by Cambridge University Press: January 2011. Research partially supported by the University of Paderborn, Germany and AFOSR grant FA9550-08-1-0173
Funding AgencyGrant Number
University of PaderbornUNSPECIFIED
Air Force Office of Scientific Research (AFOSR)FA9550-08-1-0173
Subject Keywords: Optimal control; discrete mechanics; discrete variational principle; convergence
Issue or Number:2
Classification Code:MSC: 49M25; 49N99; 65K10
Record Number:CaltechAUTHORS:20110707-075800302
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Official Citation:ESAIM: Control, Optimisation and Calculus of Variations / Volume 17 / Issue 02, April 2011, pp 322 - 352 (31 pages) Published online by Cambridge University Press: 2011 DOI:10.1051/cocv/2010012
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:24326
Deposited By: Ruth Sustaita
Deposited On:11 Jul 2011 14:59
Last Modified:03 Oct 2019 02:55

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