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Indefinite metric spaces in estimation, control and adaptive filtering

Hassibi, Babak (1996) Indefinite metric spaces in estimation, control and adaptive filtering. PhD thesis, Stanford University. http://resolver.caltech.edu/CaltechAUTHORS:20150302-072815805

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Abstract

The goal of this thesis is two-fold: first to present a unified mathematical framework (based upon optimization in indefinite metric spaces) for a wide range of problems in estimation and control, and second, to motivate and introduce the problem of robust estimation and control, and to study its implications to the area of adaptive signal processing. Robust estimation (and control) is concerned with the design of estimators (and controllers that have acceptable performance in the face of model uncertainties and lack of statistical information, and can be considered an outgrowth and extension of (the now classical) LQG theory, developed in the 1950's and 1960's which assumed perfect models and complete statistical knowledge. It has particular significance in adaptive signal processing where one needs to cope with time-variations of system parameters and to compensate for lack of a priori knowledge of the statistics of the input data and disturbances. One method of addressing the above problem is the so-called H∞ approach, which was introduced by G. Zames in 1980 and that has been recently solved by various authors. Despite the "fundamental differences" between the philosophies of the H∞ and LQG approaches to control and estimation, there are striking "formal similarities" between the controllers and estimators obtained from these two methodologies. In an attempt to explain these similarities, we shall describe a new approach to H∞ estimation (and control), different from the existing (e.g., interpolation-theoretic-based, game-theoretic-based, etc) approaches, that is based upon setting up estimation (and control problems) not in the usual Hilbert space of random variables, but in an indefinite (so-called Krein) space.


Item Type:Thesis (PhD)
Additional Information:Thesis (Ph. D.)--Stanford University, 1996. Submitted to the Department of Electrical Engineering. Copyright by the author.
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UMI9702904
Record Number:CaltechAUTHORS:20150302-072815805
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20150302-072815805
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:55375
Collection:CaltechAUTHORS
Deposited By: Shirley Slattery
Deposited On:04 Mar 2015 18:18
Last Modified:04 Mar 2015 18:18

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