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An optimal control formulation for inviscid incompressible ideal fluid flow

Bloch, Anthony M. and Holm, Darryl D. and Crouch, Peter E. and Marsden, Jerrold E. (2000) An optimal control formulation for inviscid incompressible ideal fluid flow. In: Proceedings of the 39th IEEE Conference on Decision and Control. Proceedings IEEE Conference on Decision and Control. IEEE , Piscataway, NJ, pp. 1273-1278. ISBN 0-7803-6638-7 http://resolver.caltech.edu/CaltechAUTHORS:20101008-083645353

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Abstract

In this paper we consider the Hamiltonian formulation of the equations of incompressible ideal fluid flow from the point of view of optimal control theory. The equations are compared to the finite symmetric rigid body equations analyzed earlier by the authors. We discuss various aspects of the Hamiltonian structure of the Euler equations and show in particular that the optimal control approach leads to a standard formulation of the Euler equations – the so-called impulse equations in their Lagrangian form. We discuss various other aspects of the Euler equations from a pedagogical point of view. We show that the Hamiltonian in the maximum principle is given by the pairing of the Eulerian impulse density with the velocity. We provide a comparative discussion of the flow equations in their Eulerian and Lagrangian form and describe how these forms occur naturally in the context of optimal control. We demonstrate that the extremal equations corresponding to the optimal control problem for the flow have a natural canonical symplectic structure.


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Additional Information:© 2000 IEEE. Research partially supported by the NSF and AFOSR. Work supported in part by NSF and NATO. Work supported in part by DOE Research partially supported by NSF and AFOSR. We would like to thank Peter Smereka for useful conversations.
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Air Force Office of Scientific Research (AFOSR)UNSPECIFIED
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Department of Energy (DOE)UNSPECIFIED
Subject Keywords:Euler equations , Eulerian impulse density , Hamiltonian formulation , Hamiltonian structure , Lagrangian form , finite symmetric rigid body equations , flow equations , impulse equations , inviscid incompressible ideal fluid flow , maximum principle , natural canonical symplectic structure , optimal control formulation
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INSPEC Accession Number6950490
Record Number:CaltechAUTHORS:20101008-083645353
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20101008-083645353
Official Citation:Bloch, A.M.; Holm, D.D.; Crouch, P.E.; Marsden, J.E.; , "An optimal control formulation for inviscid incompressible ideal fluid flow," Decision and Control, 2000. Proceedings of the 39th IEEE Conference on , vol.2, no., pp.1273-1278 vol.2, 2000 doi: 10.1109/CDC.2000.912030
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20344
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:23 Nov 2010 00:24
Last Modified:26 Dec 2012 12:30

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