Canonical Parametrization of the Dual Problem in Robust Optimization: Non-Rational Case
Author
Summary, in English
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.
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.
Department/s
Publishing year
2007
Language
English
Pages
2768-2775
Publication/Series
Proceedings of the European Control Conference 2007
Document type
Conference paper
Topic
- Mathematics
Keywords
- nu-gap metric
- convex duality
- robust optimization
- non-rational systems
Conference name
European Control Conference, 2007
Conference date
2007-07-02 - 2007-07-05
Conference place
Kos, Greece
Status
Published
ISBN/ISSN/Other
- ISBN: 978-960-89028-5-5