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Elementary solutions for the H infinity- general distance problem- equivalence of H2 and H infinity optimization problems


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/y2q9-nq75.


This thesis addresses the H[infinity] optimal control theory. It is shown that SISO H[infinity] optimal control problems are equivalent to weighted Wiener-Hopf 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 state-space expression for it is obtained. An interpretation of the weight as the worst-case 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 four-block general distance problem can be treated as a one-block problem. Using this result an elementary method is introduced to find a parameterization for all solutions to the four-block problem for a performance level [gamma].

The set of optimal solutions for the four-block GDP is obtained by treating the problem as a one-block 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):
  • Sideris, Athanasios
Thesis Committee:
  • Sideris, Athanasios (chair)
  • Doyle, John Comstock
  • Morari, Manfred
  • McEliece, Robert J.
  • Abu-Mostafa, Yaser S.
Defense Date:12 June 1989
Record Number:CaltechETD:etd-05152007-142515
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1824
Deposited By: Imported from ETD-db
Deposited On:15 May 2007
Last Modified:19 Apr 2021 22:25

Thesis Files

PDF (Kavranoglu_d_1990.pdf) - Final Version
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