# Identification of an LFT uncertainty model by minimizing the nu-gap metric

A4 Conference proceedings

Internal Authors/Editors

Publication Details

List of Authors: Kurt E. Häggblom

Editors: Anon

Place: New York, NY, USA

Publication year: 2014

Publisher: The Institute of Electrical and Electronics Engineers

Book title: Proceedings of the 2014 European Control Conference (ECC)

Start page: 246

End page: 251

ISBN: 978-3-9524269-1-3

Abstract

An uncertainty model in the form of a linear fractional transformation (LFT) is composed of a nominal model augmented by an uncertainty description. The size of the uncertainty required to cover a given set of models depends not only on the set of models, but also on the nominal model. Thus, the size of the uncertainty can be minimized by choosing the nominal model optimally according to some metric. If the uncertainty model is to be used for control design, a suitable metric is the nu-gap metric. It is shown that the optimal solution in terms of the nu-gap metric has to satisfy a bilinear matrix inequality (BMI) for every model in the model set. To solve this non-convex optimization problem, the BMIs are linearized to enable an iterative solution constrained by linear matrix inequalities (LMIs), where each iteration is a convex optimization problem. It is proved that the iteration converges to the optimal solution satisfying the BMIs. Because the solution is obtained as the frequency response at selected frequencies, the final model is determined by fitting a model to the frequency responses. A state-space model is used because the fitting can then easily be done subject to the same BMIs/LMIs to guarantee an optimal model. The procedure is illustrated by an application to uncertainty modeling of the product composition dynamics of a distillation column.

Keywords

LMI/BMI/SOS techniques, Mathematical modeling, Nu-gap metric, System identification, Uncertain systems

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