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
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Additional details
- Eprint ID
- 20344
- Resolver ID
- CaltechAUTHORS:20101008-083645353
- NSF
- Air Force Office of Scientific Research (AFOSR)
- NATO
- Department of Energy (DOE)
- Created
-
2010-11-23Created from EPrint's datestamp field
- Updated
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2021-11-08Created from EPrint's last_modified field
- Series Name
- Proceedings IEEE Conference on Decision and Control
- Other Numbering System Name
- INSPEC Accession Number
- Other Numbering System Identifier
- 6950490