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TESTING March 18, 2026

Data-Driven Estimation of Vinnicombe metric

Authors

Margarita A. Guerrero, Henrik Sandberg, Cristian R. Rojas

Abstract

Quantifying model mismatch in a control-relevant manner is fundamental in robust control. A well-known metric for this purpose is the $ν$-gap, or Vinnicombe metric, which measures the discrepancy between a nominal model and the real system from a closed-loop viewpoint. However, its computation typically requires explicit knowledge of the true system. In this letter, we propose an identification-free, data-driven method to estimate the $ν$-gap between discrete-time SISO systems directly from input-output experiments. The method is complemented by a data-driven winding-number test, based on Welch-type averaging, to verify a required topological condition for the computation of the metric. Numerical simulations on heavy-duty gas-turbine models and a textbook example show that the proposed estimate closely matches MATLAB$^©$ \texttt{gapmetric}, while correctly detecting cases in which the admissibility conditions fail.

Metadata

arXiv ID: 2603.17545
Provider: ARXIV
Primary Category: math.OC
Published: 2026-03-18
Fetched: 2026-03-19 06:01

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