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Canonical Parametrization of the Dual Problem in Robust Optimization: Non-Rational Case

Iantchenko, Svetlana LU and Ghulchak, Andrey LU (2007) European Control Conference, 2007 In Proceedings of the European Control Conference 2007 p.2768-2775
Abstract
In this paper, we consider the problem of robust optimization for a system with uncertainty of rank one. The main result is the canonical parameterization of all destabilizing uncertainties in the dual problem. The corresponding result in the rational case has been

previously stated in terms of unstable zero-pole cancellations.In this paper the result is extended to the class of non-rational systems with continuous nominal factors. For non-rational systems the situation with the common zeros is more complicated. The nominal

factors can contain a singular component and cannot be treated by unstable cancellations. We have shown that in the general case the common zeros of the plant factors are naturally replaced by a scalar... (More)
In this paper, we consider the problem of robust optimization for a system with uncertainty of rank one. The main result is the canonical parameterization of all destabilizing uncertainties in the dual problem. The corresponding result in the rational case has been

previously stated in terms of unstable zero-pole cancellations.In this paper the result is extended to the class of non-rational systems with continuous nominal factors. For non-rational systems the situation with the common zeros is more complicated. The nominal

factors can contain a singular component and cannot be treated by unstable cancellations. We have shown that in the general case the common zeros of the plant factors are naturally replaced by a scalar function with the positive winding number. The result has certain similarities with the parameterization of the classical Nehari problem. To illustrate the duality principle, the result is applied to a system with delay. The dual problem can be interpreted as the shortest distance from the nominal plant to all non-stabilizable plants in some metric that has a strong connection to and may be considered as a generalization of the nu-gap metric. (Less)
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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
nu-gap metric, convex duality, robust optimization, non-rational systems
in
Proceedings of the European Control Conference 2007
pages
8 pages
conference name
European Control Conference, 2007
ISBN
978-960-89028-5-5
language
English
LU publication?
yes
id
56e33161-e68a-45fa-84fb-681d18e428f6 (old id 778086)
date added to LUP
2008-01-14 15:47:25
date last changed
2016-07-08 09:39:25
@inproceedings{56e33161-e68a-45fa-84fb-681d18e428f6,
  abstract     = {In this paper, we consider the problem of robust optimization for a system with uncertainty of rank one. The main result is the canonical parameterization of all destabilizing uncertainties in the dual problem. The corresponding result in the rational case has been<br/><br>
previously stated in terms of unstable zero-pole cancellations.In this paper the result is extended to the class of non-rational systems with continuous nominal factors. For non-rational systems the situation with the common zeros is more complicated. The nominal<br/><br>
factors can contain a singular component and cannot be treated by unstable cancellations. We have shown that in the general case the common zeros of the plant factors are naturally replaced by a scalar function with the positive winding number. The result has certain similarities with the parameterization of the classical Nehari problem. To illustrate the duality principle, the result is applied to a system with delay. The dual problem can be interpreted as the shortest distance from the nominal plant to all non-stabilizable plants in some metric that has a strong connection to and may be considered as a generalization of the nu-gap metric.},
  author       = {Iantchenko, Svetlana and Ghulchak, Andrey},
  booktitle    = {Proceedings of the European Control Conference 2007},
  isbn         = {978-960-89028-5-5},
  keyword      = {nu-gap metric,convex duality,robust optimization,non-rational systems},
  language     = {eng},
  pages        = {2768--2775},
  title        = {Canonical Parametrization of the Dual Problem in Robust Optimization: Non-Rational Case},
  year         = {2007},
}