Computation and Control: Proceedings of the Bozeman Conference, Bozeman, Montana, August 1–11, 1988

406 Pages·1989·12.78 MB·English

by  Kenneth Bowers

Progress in Systems and Control Theory
Volume 1
Series Editor
Christopher I. Byrnes, Washington University
Associate Editors
S.-I. Amari, University of Tokyo, Japan
B.D.O. Anderson, Australian National University, Canberra, Australia
Karl J. Astrom, Lund Institute of Technology, Lund, Sweden
Jean-Pierre Aubin, CEREMADE, Paris, France
H.T. Banks, University of Southern California, Los Angeles, California
John S. Baras, University of Maryland, College Park, Maryland
A. Bensoussan, INRIA, Paris, France
John Bums, Virginia Polytechnic Institute, Blacksburg, Virginia
Han-Fu Chen, Beijing University, People's Republic of China
M.H.A. Davis, Imperial College of Science and Technology, London,
England
Wendell Fleming, Brown University, Providence, Rhode Island
Michel Fliess, CNRS-ESE, Gif-sur-Yvette, France
Keith Glover, University of Cambridge, Cambridge, England
D. Hinrichsen, University of Bremen, Federal Republic of Germany
Alberto Isidori, University of Rome, Italy
B. Jakubzcyk, Academy of Sciences, Warsaw, Poland
Hidenori Kimura, Osaka University, Japan
Arthur Krener, University of California, Davis
H. Kunita, Kyushu University, Japan
Alexandre Kurzhansky, IIASA, Laxenburg, Austria
Harold M. Kushner, Brown University, Providence, Rhode Island
Anders Lindquist, Royal Institute of Technology, Stockholm, Sweden
Andrzej Manitius, George Mason University, Fairfax, Virginia
Clyde F. Martin, Texas Tech University, Lubbock, Texas
Sanjoy Mitter, Massachusetts Institute of Technology, Cambridge,
Massachusetts
Giorgio Picci, LADSEB-CNR, Padova, Italy
Hector Sussman, Rutgers University, New Brunswick, New Jersey
T.J. Tam, Washington University, St. Louis, Missouri
Pravin P. Varaiya, University of California, Berkeley
Jan C. Willems, University of Groningen, Sweden
W.M. Wonham, University of Toronto, Canada
K. Bowers J. Lund
Computation
and Control
Proceedings of the
Bozeman Conference,
Bozeman, Montana,
August 1-11, 1988
With 26 Illustrations
1989 Birkhauser
Boston . Basel . Berlin
Kenneth Bowers lohn Lund
Department of Mathematics Department of Mathematics
Montana State University Montana State University
Bozeman, Montana 59717-0001 Bozeman, Montana 59717-0001
U.S.A. U.S.A.
Library of Congress Cataloging-in-Publication Data
Computation and control.
(Progress in systems and control theory; v. I)
"Collection of papers ... delivered at the first
Bozeman Conference on Computation and Control. held at
Montana State University"-Pref.
Includes bibliographies.
I. Engineering mathematics-Congresses. 2. Feedback
control systems-Congresses. I. Bowers. K. L.
(Kenneth L.) II. Lund. J. (John) III. Bozeman
Conference on Computation and Control (I st : 1988 :
Montana State University) IV. Series.
TA329.C645 1989 629.8'3 89-15743
ISBN-13:978-0-8176-3438-4
Printed on acid-free paper.
© Birkhliuser Boston. 1989
Softcover reprint of the hardcover 1st edition 1989
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ISBN-13:978-0-8176-3438-4 e-ISBN -13: 978-1-4612-3704-4
DOl: 10.1007/978-1-4612-3704-4
Text prepared by editor in camera-ready form.
9 8 7 654 3 2 I
PREFACE
The problem of developing a systematic approach to the design of feed
back strategies capable of shaping the response of complicated dynamical
control systems illustrates the integration of a wide variety of mathemat
ical disciplines typical of the modern theory of systems and control. As
a concrete example, one may consider the control of fluid flow across an
airfoil, for which recent experiments indicate the possibility of delaying
the onset of turbulence by controlling viscosity through thermal actuators
located on the airfoil. In general, there are two approaches to the con
trol of such a complica.ted process, the development of extremely detailed
models of the process followed by the derivation of a more "dedicated" feed
back law or the development of a more simple model class followed by the
derivation of control laws which are more robust to unmodelled dynamics
and exogeneous disturbances. In either approach, the two twin themes of
approximation and computation play a significant role in the derivation
and implementation of resulting control laws. And there is no doubt that
the cross-fertilization between these twin themes and control theory will
increase unabated throughout the next decade, not just as an important
component of design and implementation of control laws but also as a source
of new problems in computational mathematics.
In this volume, we present a collection of papers which were deliv
ered at the first Bozeman Conference on Computation and Control, held
at Montana State University on August 1-11, 1988. The purpose of this
conference was to bring together experts from each of these two fields in
an environment where new cross-fertilization could be fostered. Indeed, the
papers in this volume, which attest to the vitality of the interrelationship of
these two fields, contain both applications of computation and control and
the description of new trends and techniques which provide research oppor
tunities for significant new cross-fertilization. It is a pleasure to thank the
contributors, especially our four plenary speakers, Professors C.l. Byrnes,
W. Gautschi, C.F. Martin and F. Stenger, for making the conference and
the proceedings such a success.
We would like to formally acknowledge the generous support for this
conference which we received from the Office of Naval Research, Montana
State University Foundation and NSF-MONTS. We are also very grateful
for the financial and technical support provided for this conference by the
chairman and staff of the Department of Mathematical Sciences at Montana
State University.
Kenneth L. Bowers and John Lund
Bozeman, April 7, 1989
CONTENTS
Preface
Simultaneous Stabilization of Linear Time Varying Systems
by Linear Time Varying Compensation
P.R. Bouthellier and B.K. Ghosh 1
Robust Feedback Stabilization of Nonlinear Systems
C.I. Byrnes, X. Hu, and A. Isidori 11
Feedback Design from the Zero Dynamics Point of View
t C.I. Byrnes and A. Isidori 23
Two Examples of Stabilizable Second Order Systems
W.P. Dayawansa and C.F. Martin 53
Orthogonality - Conventional and Unconventional
in Numerical Analysis
t
W. Gautschi 63
Discrete Observability of Parabolic Initial Boundary Value Problems
D.S. Gilliam and C.F. Martin 97
Numerical Optimal Control via Smooth Penalty Functions
M. Hasan, B.N. Lundberg, A.B. Poore, and B. Yang 105
Observability and Inverse Problems Arising in Electrocardiography
I. Iakovidis, C.F. Martin, and S. Xie 117
Eigenvalue Approximations on the Entire Real Line
M. Jarratt 133
Prediction Bands for Ill-Posed Problems
A. Jonca 145
Controllability, Approximations and Stabilization
M. Kawski 155
t Plenary Lecture Series
CONTENTS
Interval Mathematics Techniques for Control Theory Computations
R.B. Kearfott 169
Accuracy and Conditioning in the Inversion of the Heat Equation
~L~d IN
On the Recovery of Surface Temperature and Heat Flux
via Convolutions
B.A. Mair 197
Observability, Interpolation and Related Topics
t C.F. Martin 209
Constructing Polynomials over Finite Fields
C.F. Martin and M. Stamp 233
A Collocative Variation of the Sinc-Galerkin Method
for Second Order Boundary Value Problems
K.M. McArthur 253
A Sine-Collocation Method for Weakly Singular
Volterra Integral Equations
B. V. Riley 263
Tuning Natural Frequencies by Output Feedback
J. Rosenthal 277
Efficient Numerical Solution of Fourth-Order Problems
in the Modeling of Flexible Structures
R.C. Smith, K.L. Bowers, and J. Lund 283
Explicit Approximate Methods for Computational Control Theory
t F. Stenger 299
Sine Approximate Solution of Quasilinear Equations
of Conservation Law Type
M. Stromberg 317
Systems with Fast Chaotic Components
T.J.S. Taylor 333
t Plenary Lecture Series
CONTENTS
Bifurcation and Persistance of Minima in Nonlinear
Parametric Programming
C.A. Tiahrt and A.B. Poore 343
Numerical Solution of an Ill-Posed Coefficient
Identification Problem
C.R. Vogel 355
Observability, Predictability and Chaos
D.l. Wallace 365
Geometric Inverse Eigenvalue Problem
x.
Wang 375
Observability and Group Representation Theory
J.A. Wolf 385
Highly-Accurate Difference Schemes for Solving
Hyperbolic Problems
G. Yin 393
A Finite Spectrum Unmixing Set for 9£(3, R)
x.-J.
Zhu 403
CONTRmUTORS
Paul Bouthellier, Department of Systems Science and Mathematics,
Washington University, St. Louis, Missouri 63130
Ken Bowers, Department of Mathematical Sciences, Montana State
University, Bozeman, Montana 59717
Ohris Byrnes, Department of Mathematics, Arizona State
University, Tempe, Arizona 85287
Wijesuriya Dayawansa, Department of Mathematics, Texas Tech
University, Lubbock, Texas 79409
Walter Gautschi, Department of Computer Science, Purdue
University, West Lafayette, Indiana 47907
Bijoy Ghosh, Department of Systems Science and Mathematics,
Washington University, St. Louis, Missouri 63130
Dave Gilliam, Department of Mathematics, Texas Tech University,
Lubbock, Texas 79409
Mohammed Hasan, Department of Mathematics, Colorado State
University, Fort Collins, Colorado 80523
Xiao-Ming Hu, Department of Mathematics, Arizona State
University, Tempe, Arizona 85287
Ilias Iakovidis, Department of Mathematics, Texas Tech University,
Lubbock, Texas 79409
Alberto Isidori, Department d'Informatica e Sistemistica, Universita di
Roma - "La Sapienza" , Via Eudossiana 18, 00 184 Roma, Italy
Mary Jarratt, Department of Mathematics, Boise State University,
Boise, Idaho 83725
Andrzej Jonca, Department of Mathematics, Long Beach State
University, Long Beach, California 90840
CONTRIBUTORS
Matthias Kawski, Department of Mathematics, Arizona State
University, Tempe, Arizona 85287
Baker Kearfott, Department of Mathematics, University of
Southwestern Louisiana, Lafayette, Louisiana 70504
John Lund, Department of Mathematical Sciences, Montana State
University, Bozeman, Montana 59717
Bruce Lundberg, Department of Mathematics, Colorado State
University, Fort Collins, Colorado 80523
Bernard Mair, Department of Mathematics, Texas Tech University,
Lubbock, Texas 79409
Clyde Martin, Department of Mathematics, Texas Tech University,
Lubbock, Texas 79409
Kelly McArthur, Department of Mathematics, University of Utah,
Salt Lake City, Utah 84112
Aubrey Poore, Department of Mathematics, Colorado State
University, Fort Collins, Colorado 80523
Bruce Riley, Department of Mathematics, University of Wisconsin
at LaCrosse, LaCrosse, Wisconsin 54601
Joachim Rosenthal, Department of Mathematics, Arizona State
University, Tempe, Arizona 85287
Ralph Smith, Department of Mathematical Sciences, Montana
State University, Bozeman, Montana 59717
Mark Stamp, Department of Mathematics, Texas Tech University,
Lubbock, Texas 79409
Frank Stenger, Department of Mathematics, University of Utah,
Salt Lake City, Utah 84112
Marc Stromberg, Department of Mathematics, Texas Tech
University, Lubbock, Texas 79409