An explicit state-space solution to the one-block super-optimal distance problem
File(s)
Author(s)
Kiskiras, J
Jaimoukha, IM
Halikias, GD
Type
Journal Article
Abstract
An explicit state-space approach is presented for solving the super-optimal Nehari-extension problem. The approach is based on the all-pass dilation technique developed in [JL93] which offers considerable advantages compared to traditional methods relying on a diagonalisation procedure via a Schmidt pair of the Hankel operator associated with the problem. As a result, all derivations presented in this work rely only on simple linear-algebraic arguments. Further, when the simple structure of the one-block problem is taken into account, this approach leads to a detailed and complete state-space analysis which clearly illustrates the structure of the optimal solution and allows for the removal of all technical assumptions (minimality, multiplicity of largest Hankel singular value, positive-definiteness of the solutions of certain Riccati equations) made in previous work [LHG89],[HLG93]. The advantages of the approach are illustrated with a numerical example. Finally, the paper presents a short survey of super-optimization, the various techniques developed for its solution and some of its applications in the area of modern robust control.
Editor(s)
Grüne, L
Date Issued
2013-06
Citation
Mathematics of Control, Signals and Systems (MCSS), 2013, 25 (2), pp.167-196
ISSN
0932-4194
Publisher
Springer
Start Page
167
End Page
196
Journal / Book Title
Mathematics of Control, Signals and Systems (MCSS)
Volume
25
Issue
2
Copyright Statement
The final publication is available at Springer via http://dx.doi.org/10.1007/s00498-012-0097-8
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=000317986300002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Subjects
super-optimal Nehari-extension problems
Hankel operator
all-pass dilations
H_infinity optimal control
maximally robust stabilization
Publication Status
Published