Uncertainty, complication and optimal model construction
Issaevitch, Thomas Alan
This item is only available for download by members of the University of Illinois community. Students, faculty, and staff at the U of I may log in with your NetID and password to view the item. If you are trying to access an Illinois-restricted dissertation or thesis, you can request a copy through your library's Inter-Library Loan office or purchase a copy directly from ProQuest.
Permalink
https://hdl.handle.net/2142/30819
Description
Title
Uncertainty, complication and optimal model construction
Author(s)
Issaevitch, Thomas Alan
Issue Date
1998
Director of Research (if dissertation) or Advisor (if thesis)
Oono, Yoshitsugu
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
control system
optimal model construction
uncertainty
Language
en
Abstract
"I consider the problem of determining optimal knowledge partitions in problems described
by complicated models with associated embedded optimization requirements. The particular
models studied are linear control models in which the embedded optimization is that of
observer/ controller design.
The existence of an optimal knowledge partition rests on the tradeoff between the gain in
accuracy achieved by more knowledge about a system offset by the increased complication that
knowledge typically brings (""information oyerload"" ). Thus, even though increased knowledge
I
will always result in a true optimum that is superior, the increased complication (and nonzero
computation costs) may make finding that optimum practically impossible.
With the reduction of complication achieved by eliminating knowledge, one automatically
experiences an increase of uncertainty. Thus, the possibility of actually correctly reducing
complication requires that one have a theory capable of handling the uncertainty. In control
theory, while control under uncertainty is an extremely important field with many deep
results, until now there was no theory providing a nonperturbative optimal control law for
uncertain Stochastic Linear Quadratic Regulator systems. My first result creates such a
theory.
In order to obtain an explicit example of how one can determine an optimal knowledge
partition, I study a simple control system - the iso-spectral system. For this system, it is
explicitly demonstrated that the controller design problem is equivalent to a spin-glass of
Sherrington-Kirkpatric type. Using this result, I prove that a nontrivial optimal knowledge
partition can exist and give a prescription for determining locally optimal optimal knowledge
partitions. That a model as simple as the iso-spectral system leads to an optimization problem equivalent
to finding the ground state of a spin--glass is an indication that the possible existence
of an optimal knowledge partition should always be considered."
Use this login method if you
don't
have an
@illinois.edu
email address.
(Oops, I do have one)
IDEALS migrated to a new platform on June 23, 2022. If you created
your account prior to this date, you will have to reset your password
using the forgot-password link below.
