Optimization and Control Seminar, Fall 2007
| Thursday, Sept. 27, 2007, 11:00-12:00 pm |
SOND 414 |
Extremal Ellipsoids of Convex Bodies and Their Symmetry Properties
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| - Dr. Osman Guler |
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| Abstract: A convex body K is a compact convex set in $R^n$ which has an interior.
It is known that K has a unique circumscribed ellipsoid MVCE(K) and a unique
inscribed ellipsoid MVIE(K). The former contains K and has minimum volume, and
the latter is contained in K and has maximum volume.
The two ellipsoids crop up in many different fields under different
disguises.
In this talk, we first develop the basic properties the the ellipsoids using
semi-infinite programming. The uniqueness of the ellipsoids have the important
property that they inherit the symmetry poperties of K.
The seond part of the talk will be about the symmetry properties convex
bodies and ellipsoids.
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| Monday, Oct. 1, 2007, 11:00-12:00 pm |
SOND 414 |
| Switching control of transport on a graph (joint with the DE seminar) |
| - Dr. Tom Seidman |
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| Abstract: We consider a hybrid system
(mixed state: discrete and
continuous) for which the continuous dynamics model quasilinear
transport on a graph and the discrete dynamics model a sequence
of control actions. switching between available `modes' of the
system. After commenting on the modelling, we show the well-
posedness of the system (with switching as data), existence of
an optimal control, and "hybrid well-posedness" of a feedback
implementation. |
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