Thermal-Fluid Control via Finite-Dimensional Approximation
Ajit R. Shenoy
Eugene M. Cliff
Aerospace and Ocean Engineering Deptartment
Virginia Polytechnic Institute and State University
Matthias Heinkenschloss
Department of Mathematics
Virginia Polytechnic Institute and State University
ICAM Report 96-04-01
April 1996
AIAA Paper 96--1910
31st AIAA Thermophysics Conference
June 17-20, 1996 / New Orleans, LA
Abstract
We formulate a thermal-fluid control problem wherein the physics are
described by a system of partial differential equations and the control
enters through a thermal boundary condition. A finite-element
approximation is used to transcribe this to a finite-dimensional Quadratic
Programming problem. The finite-dimensional problem displays an expected
sparcity pattern in the Jacobian of the constraints and the Hessian of the
cost function. Three versions of the QP problem are considered -- these
differ in their treatment of certain control bounds. Numerical studies
show that variants which faithfully reflect the structure of control bounds
in the infinite-dimensional problem lead to well-behaved QP solutions,
while variants that do not are troublesome for the QP algorithm. It is
somewhat surprising that this behavior is apparent even when the
finite-element grid is relatively coarse.
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