An Optimal Control Problem for Flows with Discontinuities
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
Ajit R. Shenoy
Aerospace and Ocean Engineering Deptartment
Virginia Polytechnic Institute and State University
Journal of Optimization Theory and Applications,
Vol 94, 1997, pp. 273-309.
Abstract
In this paper we study a design problem for a duct flow with a
shock. The presence of the shock
often causes numerical difficulties.
Good shock capturing schemes with low continuity properties often
can not be combined successfully with efficient optimization
methods requiring smooth functions.
A remedy studied in this paper is to introduce the shock location
as an explicit variable. This allows one to fit the shock and
yields a problem with sufficiently often differentiable functions.
We prove the existence of optimal solutions, the \frechet
differentiability, and the existence of Lagrange multipliers.
In the second part we introduce and investigate the discrete problem
and study the relations between the optimality conditions for the
infinite dimensional problem and the discretized one.
This reveals information important for the numerical solution of the
problem. Numerical examples are given to demonstrate the theoretical
findings.
Keywords
Optimal control, Euler flow equations, sequential quadratic programming.
AMS subject classifications
49M37, 49K15
PDF file (297kB)
of the ICAM Report 95-09-02
September 1995 (revised February 1996).
The JOTA paper is a shortened version of this report.