Citation
Kavranoglu, Davut (1990) Elementary solutions for the H infinity general distance problem equivalence of H2 and H infinity optimization problems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/y2q9nq75. https://resolver.caltech.edu/CaltechETD:etd05152007142515
Abstract
This thesis addresses the H[infinity] optimal control theory. It is shown that SISO H[infinity] optimal control problems are equivalent to weighted WienerHopf optimization in the sense that there exists a weighting function such that the solution of the weighted H2 optimization problem also solves the given H[infinity] problem. The weight is identified as the maximum magnitude Hankel singular vector of a particular function in H[infinity] constructed from the data of the problem at hand, and thus a statespace expression for it is obtained. An interpretation of the weight as the worstcase disturbance in an optimal disturbance rejection problem is discussed.
A simple approach to obtain all solutions for the Nehari extension problem for a given performance level [gamma] is introduced. By a limit taking procedure we give a parameterization of all optimal solutions for the Nehari's problem.
Using an imbedding idea [12], it is proven that fourblock general distance problem can be treated as a oneblock problem. Using this result an elementary method is introduced to find a parameterization for all solutions to the fourblock problem for a performance level [gamma].
The set of optimal solutions for the fourblock GDP is obtained by treating the problem as a oneblock problem. Several possible kinds of optimality are identified and their solutions are obtained.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Degree Grantor:  California Institute of Technology 
Division:  Engineering and Applied Science 
Major Option:  Electrical Engineering 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  12 June 1989 
Record Number:  CaltechETD:etd05152007142515 
Persistent URL:  https://resolver.caltech.edu/CaltechETD:etd05152007142515 
DOI:  10.7907/y2q9nq75 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  1824 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  15 May 2007 
Last Modified:  19 Apr 2021 22:25 
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