Optimal Design and Control: Proceedings of the Workshop on Optimal Design and Control Blacksburg, Virginia April 8–9, 1994

297 Pages·1995·6.64 MB·English

by  Natalia Alexandrov

Progress in Systems and Control Theory
Volume 19
Series Editor
Christopher I. Byrnes, Washington University
Optimal Design and Control
Proceedings of the Workshop
on Optimal Design and Control
Blacksburg, Virginia
April8-9, 1994
Jeffrey Borggaard, John Burkardt,
Max Gunzburger, and J anet Peterson
Editors
Springer Science+Business Media, LLC
Editors:
Jeffrey Borggaard
John Burkardt
Max Gunzburger
Janet Peterson
Air Force Center for Optimal Design and Control
Interdisciplinary Center for Applied Mathematics
Virginia Tech
Blacksburg, Virginia 24061-0531
Library ofCongress Cataloging In-Publication Data
Workshop on Optimal Design and Control (1994 : Blacksburg, VA.)
Optimal design and control : proceedings of the workshop on
Optimal Design and Control, Blacksburg, Virginia, April8-9, 1994 /
Jeffrey Borggaard ... [et al.], editors.
p. cm. --(Progress in systems and control theory ; v. 1~J)
Includes bibliographical references.
ISBN 978-1-4612-6916-8 ISBN 978-1-4612-0839-6 (eBook)
DOI 10.1007/978-1-4612-0839-6
1. Automatic control--Congresses. 2. Mathematical optimization-
-Congresses. 1. Borggaard, Jeffrey, 1964- II. Title.
III. Series.
TJ212.W675 1994 95-10230
629.8--dc20 CIP
Printed on acid-free paper
© 1995 Springer Science+Business Media New York
Originally published by Birkhiluser Boston in 1995
Softcover reprint ofthe hardcover lst edition 1995
Copyright is not claimed for works of U.S. Government employees.
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should be addressed directly to Springer Science+Business Media, LLC.
ISBN 978-1-4612-6916-8
Typeset by the editors
CONTENTS
Contributors Vll
Preface. . . xi
Multilevel Algorithms for Nonlinear Optimization
N. Alexandrov and 1. Dennis .................. 1
Shape Optimization in One Shot
E. Arian and S. Ta'asan. . . .... 23
Computational Aspects of Differential Dynamic Programming and
Nonlinear Programming Techniques for Optimal Control
1. Arora, D. Holtz, and N. Kota. . . . . . . . . . . . . . . . . 41
Optimal Control of Metal Forging
J. Berg, R. Adams, J. Malas, and S. Banda . 55
The Application of Sparse Least Squares in Aerospace Design Problems
1. Betts . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Algorithms for Flow Control and Optimization
J. Borggaard, J. Burkardt, J. Burns, E. Cliff, M. Gunzburger,
H. Kim, H. Lee, J. Peterson, A. Shenoy, and X. Wu . . . . . 97
Generalized Reduced Gradient Algorithm for Large-scale
Trajectory Optimization Problems
K. Brenan and W Hallman . . . . . . . . . .. ..... 117
The Optimal Design Problem of Cea and Malanowski Revisited
M. Delfour and J.-P. Zolesio. . . . . . . . . . . .. ... 133
Uniformly Scalar Spline Approximations for Scalar Delay Problems
R. Fabiano. . . . . . . . . . . . . . . . . . . . . . . . . 151
Implicit Filtering and Optimal Design Problems
P. Gilmore, C. Kelley, C. Miller, and G. Williams ... 159
Generating Conjugate Directions Using Limited Second Derivatives
A. Griewank and M. Fruth . . . . . . . . . . . . . . . . . . 177
VI Contents
Contact Shape Optimization
J. Haslinger . . . . . . .... 189
Optimal Control of Thermally Coupled Navier-Stokes Equations
K. Ito, 1. Scroggs, and H. Tran . . . . . . . . . . .. ... 199
Optimization Methods in the Process Control of Industrial Furnaces
H. Jager, E. Sachs, H. Heidemiiller, F. Maschler,
H. Klammer, and G. Woelk . . . . . . . . . . . . . . . . . . 215
Maximal Decay Rates and Asymptotic Behavior of
Solutions in Nonlinear Elastic Structures
1. Lasiecka and W Heyamn . . . . . . . . ... 229
Preparation of Advanced CFD Codes for use in Sensitivity Analyses
and Multidisciplinary Design Optimization
P. Newman ........................ 241
An Introduction to the Formation Theory of Active Metals
D. Russell . . . . . . . . . . . . . . . . . . . . . . . . . 275
viii Contributors
Michel C. Delfour - Centre de Recherches Matbematiques et Departement de Ma
tbematiques et de Statistique, Universite de Montreal, C.P. 6128 Succ. Cen
treville, Montreal, Quebec, H3C 3J7, Canada
J. E. Dennis, Jr. - Department of Computational and Applied Mathematics, Rice
University, P. O. Box 1892, Houston TX 77251-1892, USA
Richard H. Fabiano - Department of Mathematics, Texas A&M University, Col
lege Station TX 77843, USA
Manfred Fruth - Institute of Scientific Computing, Technisch(~ Universitat Dres
den D-0-8027 Dresden, Germany
P. Gilmore - National High Magnetic Field Laboratory, Florida State University,
Tallah.assee FL 32306-3016, USA
Andreas Griewank - Institute of Scientific Computing, Technische Universitat
Dresden D-0-8027 Dresden, Germany and Mathematics and Computer Sci
ence Division, Argonne National Laboratory, Argonne IL 60439-4844, USA
Max Gunzburger - Air Force Center for Optimal Design and Control, Interdis
ciplinary Center for Applied Mathematics, Virginia Te(:h, Blacksburg VA
24061-0531, USA
Wayne P. Hallman - The Aerospace Corporation, 2350 E. EI Segundo Blvd., EI
Segundo CA 90245, USA
Jaroslav Haslinger - KFK MFF UK, Ke Karlova 5, Faculty of Mathematics and
Physics, Charles University, 12000 Prague, The Czech Republic
H. Heidemiiller - GIWEP, Tristanstr. 12, D-45473 Millheim (Ruhr), Germany
W Heyman - Department of Applied Mathematics, University of Virginia, Char
lottesville VA 22903, USA
Dale A. Holtz - Optimal Design Laboratory, Civil and Environmental Engineer
ing, Mechanical Engineering, The University of Iowa, Iowa City IA 52242,
USA
Kazufumi Ito - Center for Research in Scientific Computation, North Carolina
State University, Raleigh NC 27695-8205, USA
H. Jager - Universitat Trier, FB IV - Mathematik, D-54286 Trier, Germany
C. T. Kelley - Department of Mathematics and Center for Research in Scientific
Computation, North Carolina State University, Raleigh NC 27695-8205
Hongchul Kim - Interdisciplinary Center for Applied Mathematics, Virginia Tech,
Blacksburg VA 24061-0531, USA
Contributors ix
H. Klammer - GIWEP, Tristanstr. 12, D-45473 Miilheim (Ruhr), Germany
Narendra N. Kota - Optimal Design Laboratory, Civil and Environmental Engi
neering, Mechanical Engineering, University of Iowa, Iowa City IA 52242,
USA
1. Lasiecka - Department of Applied Mathematics, University of Virginia, Char
lottesville VA 22903, USA
Hyung-Chun Lee - Air Force Center for Optimal Design and Control, Interdis
ciplinary Center for Applied Mathematics, Virginia Tech, Blacksburg VA
24061-0531, USA
James C. Malas III - Materials Directorate, Wright Laboratory, Wright-Patterson
Air Force Base OH 45433-7531, USA
F. Maschler - GIWEP, Tristanstr. 12, D-45473 Miilheim (Ruhr), Germany
C. T. Miller - Department of Environmental Sciences and Engineering, 105 Rose
nau Hall, University of North Carolina, Chapel Hill NC 27599-7400, USA
Perry Newman - Mail Stop 159, NASA Langley Research Center, Hampton VA
23681-000 1, USA
Janet Peterson - Air Force Center for Optimal Design and Control, Interdisciplina
ry Center for Applied Mathematics, Virginia Tech, Blacksburg VA 24061-
0531, USA
David L. Russell - Department of Mathematics, Virginia Tech, Blacksburg VA
24061-0123, USA
E. Sachs - Universitat Trier, FB IV - Mathematik, D-54286 Trier, Germany
Jeffrey S. Scroggs - Center for Research in Scientific Computation, North Car
olina State University, Raleigh NC 27695-8205, USA
Ajit Shenoy - Air Force Center for Optimal Design and Control, Interdisciplinary
Center for Applied Mathematics, Virginia Tech, Blacksburg VA 24061-0531 ,
USA
Shlomo Ta'asan - The Weizmann Institute of Science, Rehovot 76100, Israel and
Institute for Computer Applications in Science and Engineering, Mail Stop
132C, NASA Langley Research Center, Hampton VA 23681, USA
Hien T. Tran - Center for Research in Scientific Computation, Box 8205, North
Carolina State University, Raleigh NC 27695-8205, USA
x Contributors
G. A. Williams - Department of Environmental Sciences and Engineering, 105
Rosenau Hall, University of North Carolina, Chapel Hill NC 27599-7400,
USA
G. Woelk - Rhein.-Westf. Technische Hochschule Aachen, Lehrgebiet Industrie
ofenbau, Kopernikusstr. 16, D-52056 Aachen, Germany
Xianon Wu - Air Force Center for Optimal Design and ControJ, Interdisciplinary
Center for Applied Mathematics, Virginia Tech, Blacksburg VA 24061-0531 ,
USA
lean-Paul ZoJesio - Institut Non Lineaire de Nice, CNRS, 1361 Route des Luci
oles, 06904 Sophia Antipolis Cedex, France
PREFACE
This volume is the proceedings of the Workshop on Optimal Design and Control
that was held in Blacksburg, Virginia, April 8-9, 1994. The workshop was spon
sored by the Air Force Office of Scientific Research through the Air Force Center
for Optimal Design and Control (CODAC) at Virginia Tech.
The workshop was a gathering of engineers and mathematicians actively in
volved in innovative research in control and optimization, with emphasis placed on
problems governed by partial differential equations. The interdisciplinary nature
of the workshop and the wide range of subdisciplines represented by the partici
pants enabled an exchange of valuable information and also led to significant dis
cussions about multidisciplinary optimization issues. One of the goals of the work
shop was to include laboratory, industrial, and academic researchers so that anal
yses, algorithms, implementations, and applications could all be well-represented
in the talks; this interdisciplinary nature is reflected in these proceedings.
An overriding impression that can be gleaned from the papers in this volume is
the complexity of problems addressed by not only those authors engaged in appli
cations, but also by those engaged in algorithmic development and even mathemat
ical analyses. Thus, in many instances, systematic approaches using fully nonlin
ear constraint equations are routinely used to solve control and optimization prob
lems, in some cases replacing ad-hoc or empirically based procedures.
Although many different applications (e.g., metal forging, heat transfer, con
tact problems, structures, and acoustics) are addressed here, flow control plays a
central role throughout these proceedings. Optimal control of incompressible vis
cous flows and compressible flows, including flows with shock waves, are consid
ered by many of the authors.
Many algorithmic issues are addressed in these proceedings. These include
sensitivity analyses, novel optimization methods especially tailored for specific
applications, multilevel methods, and programming techniques. At times, differ
ent methods for similar problems are presented so that one can compare the dif
ferent approaches. For example, in sensitivity based optimal control algorithms,
the sensitivity equations approach and the automatic differentiation approach are
discussed. Another set of contrasting approaches are the differential equation sen
sitivity view and the discrete equation sensitivity (including grid sensitivity) ap
proach of different authors. Other algorithmic issues considered include sparse
least squares methods for aerospace design and implicit filtering.
Another recurring theme throughout these proceedings is shape control, i.e.,
the use of the shape of the boundary to effect control or to achieve an optimal con
figuration. Two papers specifically address problems in this area; one is on contact
shape optimization and another addresses issues related to the existence and com
putation of optimal domains.
xii Preface
The overall impression one is left with is that there has been significant progress
in the analysis and computation of control and optimization problems involving
complex systems, and that these results are being applied to interesting and im
portant applications. On the other hand, there are many issues that have not been
completely resolved. These include the reduction of the cost of obtaining optimal
states and controls and a more complete understanding of shape optimization for
nonlinear, three-dimensional systems. Thus, there is much interesting work still to
be done!
We would like to acknowledge the efforts of the Organizing Committee for the
Workshop on Optimal Design and Control (Bernard Grossman, John Burns, Eu
gene Cliff, Terry Herdman, and Janet Peterson, all of Virginia Tech) and Melissa
Chase for putting together the interesting and informative workshop that led to
these proceedings. We also acknowledge the support of the Aiir Force Office of
Scientific Research and, in particular, Charles Holland and Marc Jacobs of that of
fice, for supporting the Workshop under AFOSR URI Grant Number F49620-93-
1-0280.
Jeffrey Borggaard, John Burkardt
Max Gunzburger, and Janet Peterson
Blacksburg, 1995