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

• Main Author: Kavranoglu, Davut
• Format: Others
• Language: en
• Published: 1990
• Online Access: https://thesis.library.caltech.edu/1824/1/Kavranoglu_d_1990.pdf; 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. https://resolver.caltech.edu/CaltechETD:etd-05152007-142515 <https://resolver.caltech.edu/CaltechETD:etd-05152007-142515>

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.