Optimal control formulation for inviscid incompressible ideal fluid flow.

Bloch, A. M. ; Crouch, P. E.

Technical Information Center Oak Ridge Tennessee

关键词: Fluid flow;    Incompressible flow;    Inviscid;    Optimal control problem;    Optimal control;   

RP-ID  :  DE2001765583

学科分类：工程和技术（综合）

美国|英语

来源: National Technical Reports Library

【 摘 要 】

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 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 the 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.