Data-Driven Estimation of Vinnicombe metric
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| Format: | Preprint |
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2026
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| _version_ | 1866918395351400448 |
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| author | Guerrero, Margarita A. Sandberg, Henrik Rojas, Cristian R. |
| author_facet | Guerrero, Margarita A. Sandberg, Henrik Rojas, Cristian R. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_17545 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Data-Driven Estimation of Vinnicombe metric Guerrero, Margarita A. Sandberg, Henrik Rojas, Cristian R. Optimization and Control 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. |
| title | Data-Driven Estimation of Vinnicombe metric |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2603.17545 |