Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published 2000 | Published
Book Section - Chapter Open

An optimal control formulation for inviscid incompressible ideal fluid flow

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.

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.

Attached Files

Published - BlCrHoMa2000.pdf

Files

BlCrHoMa2000.pdf
Files (120.6 kB)
Name Size Download all
md5:483dd19c3ef75ed3e6c38b96006ab9cb
120.6 kB Preview Download

Additional details

Created:
August 19, 2023
Modified:
January 13, 2024