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

Author: Kavranoglu, Davut

Year: 1990

Degree: Dissertation (Ph.D.)

Advisor: Sideris, Athanasios

Committee Members: Sideris, Athanasios; Doyle, John Comstock; Morari, Manfred; McEliece, Robert J.; Abu-Mostafa, Yaser S.

Option: Electrical Engineering

DOI: 10.7907/y2q9-nq75

Abstract

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.

Files