Algorithms for worst case identification in H∞ and in the ν-gap metric

Authors:
P. Date;G. Vinnicombe
Affiliations:
Department of Mathematical Sciences, Center for Analysis of Risk and Optimisation Modelling Applications, Brunel University, UK;Department of Engineering, University of Cambridge, UK
Venue:
Automatica (Journal of IFAC)
Year:
2004

Citing 2
Cited 2

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Worst-case control-relevant identification

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System identification for achieving robust performance

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Abstract

This paper considers two robustly convergent algorithms for the identification of a linear system from (possibly) noisy frequency response data. Both algorithms are based on the same principle; obtaining a good worst case fit to the data under a smoothness constraint on the obtained model. However they differ in their notions of distance and smoothness. The first algorithm yields an FIR model of a stable system and is optimal, in a certain sense for a finite model order. The second algorithm may be used for modelling unstable plants and yields a real rational approximation in the L"2-gap. Given a model and a controller stabilising the true plant, a procedure for winding number correction is also suggested.