
GENERAL SCIENTIFIC ACTIVITIES July 1991 June 1992
Control Theory and Geometric Mechanics Program (January  July 1992)
The Institute began its scientific activities with a half year start
up program in control theory.
The program committee consists of:
Bruce Francis (Electrical Engineering Department, University of Toronto),
Ivan Kupka (Mathematics Department, University of Toronto),
William F. Shadwick (Pure Mathematics Department, University of Waterloo)
George Zames (Electrical Engineering Department, McGill University).
An overview of the control theory activity is given below.
WEEKLY SEMINAR
SERIES September 1991  July 1992
WORKSHOPS March  June 1992
June 28  30, 1992 
Workshop on Problems in Sensing, Identification and Control of Flexible
Structures
Workshop Coordinator: K.A. Morris
Flexible structures arise in several important areas of application,
for instance: antenna control, robotics and large space structures.
Satisfactory control of these systems is hampered by difficulties
related to sensing and identification. The first day of this workshop
was a short course on identification of flexible structures conducted
by Dr. JerNan Juang of the NASA Langley Research Centre. The remainder
of the workshop consisted of talks on current rearch by engineers
and mathematicians working in structural control. There was also
a tour of the flexible structuress lab facility at the University
of Waterloo.
June 12, 1992  Mechanics Day
Coordinator: J. Marsden (The Fields Institute and University of
California at Berkeley)
This worksop was a celebration of the 25th anniversary of the publication
of Foundations of Mechanics by Ralph Abraham and Jerrold
E. Marsden. It featured lectures from many people who have been
prominent in the development and application of geometric techniques
in mechanics and related areas in science and engineering.
June 69, 1992  Geometric Variational Problems and Optimal
Control
Coordinators V. Jurdjevic (University of Toronto), I. Kupka (University
of Toronto), W. Shadwick (The Fields Institute)
The interplay between geometry and variational problems is a theme
which goes back to the work of Lagrange. The problems posed by optimal
control theory, mathematical physics and differential geometry have
all led to the study of constrained variational problems from an
essentially geometric point of view. The Pontryagin Maximum Principle,
the Dirac Theory of Constraints and the GriffithsBryant approach
to geometric variational problems may all be thought of as methods
for extracting the geometric content of a constrained variational
problem. The purpose of this workshop was to bring together practitioners
from these various fields and to explore other applications of geometric
ideas and techniques in nonlinear control theory.
June 1 4, 1992 Research Seminar on the
Method of Equivalence
William F. Shadwick (University of Waterloo), Robert B. Gardner
(University of North Carolina)
May 31  June 4, 1992  Workshop
on Control of Molecular Systems
Coordinators: Mohammed Dahleh (University of California at Santa
Barbara), Anthony Peirce (McMaster University)
The application of systems theory to the control of molecular systems
is a new research area which has the potential to produce new technology
for manipulating and understanding molecular systems. This five
day workshop promoted interdisciplinary collaboration between control
theorists, physicists and chemists.
March 2931, 1992 
Workshop on Hamiltonian and Gradient Flows, Algorithms and Control
March 810, 1992 
Workshop on The Falling Cat and Related Problems
March 810, 1992 
Jerrold Marsden (Director, The Fields Institute)
Lecture
Series on Geometry and Control of Coupled Structures
May 3  7, 1992  Advanced Digital Control
Tongwen Chen (University of Calgary), Bruce Francis (University
of Toronto)
Demonstration by: Jacob Apkarian (SPAR Aerospace, Toronto)
April 8  May 13, 1992  Nonlinear Control Theory
R.B.Gardner (University of North Carolina), W.F. Shadwick (University
of Waterloo)
COURSES February  June 1992
June 1  4, 1992
Method of Equivalence
Robert B. Gardner, Mathematics Department, University of North Carolina/Fields
Institute
William F. Shadwick, Pure Mathematics Department, University of Waterloo/Fields
Institute
May 3  7, 1992
Advanced Digital Control
Tongwen Chen, Electrical Engineering Department, University of Calgary
Bruce Francis, Electrical Engineering Department, University of Toronto
Demonstration by: Jacob Apkarian, SPAR Aerospace, Toronto
April 8  May 13, 1992
Nonlinear Control Theory
Robert B. Gardner, Mathematics Department, University of North Carolina/Fields
Institute
William F. Shadwick, Pure Mathematics Department, University of Waterloo/Fields
Institute
March 8  10, 1992
Geometry and Control of Coupled Structures
Jerrold E. Marsden, Fields Institute and Mathematics Department, University
of California, Berkeley
February 12  March 18, 1992
Nonlinear Control Theory
Velimir Jurdjevic, Mathematics Department, University of Toronto
Ivan Kupka, Mathematics Department, University of Toronto
DISTINGUISHED LECTURE SERIES June 1992
June 11, 1992  held at the University of Waterloo
Phillip Griffiths (Institute for Advaced Study)
Exterior Differential Systems (general talk),
June 11, 1992 
Stephen Smale (University of California, Berkeley)
Bezout's Theorem and Complexity Theory
June 10  11, 1992 , held at the University of Waterloo
Phillip Griffiths (Institute for Advanced Study)
Characteristic Cohomology of Differential Systems; Conservation
Laws for Differential Systems
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