Data-Driven Estimation of Structured Singular Values
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915523338436608 |
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| author | Guerrero, Margarita A. Lakshminarayanan, Braghadeesh Rojas, Cristian R. |
| author_facet | Guerrero, Margarita A. Lakshminarayanan, Braghadeesh Rojas, Cristian R. |
| contents | Estimating the size of the modeling error is crucial for robust control. Over the years, numerous metrics have been developed to quantify the model error in a control relevant manner. One of the most important such metrics is the structured singular value, as it leads to necessary and sufficient conditions for ensuring stability and robustness in feedback control under structured model uncertainty. Although the computation of the structured singular value is often intractable, lower and upper bounds for it can often be obtained if a model of the system is known. In this paper, we introduce a fully data-driven method to estimate a lower bound for the structured singular value, by conducting experiments on the system and applying power iterations to the collected data. Our numerical simulations demonstrate that this method effectively lower bounds the structured singular value, yielding results comparable to the MATLAB$^©$ Robust Control Toolbox. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_13410 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Data-Driven Estimation of Structured Singular Values Guerrero, Margarita A. Lakshminarayanan, Braghadeesh Rojas, Cristian R. Systems and Control Optimization and Control Estimating the size of the modeling error is crucial for robust control. Over the years, numerous metrics have been developed to quantify the model error in a control relevant manner. One of the most important such metrics is the structured singular value, as it leads to necessary and sufficient conditions for ensuring stability and robustness in feedback control under structured model uncertainty. Although the computation of the structured singular value is often intractable, lower and upper bounds for it can often be obtained if a model of the system is known. In this paper, we introduce a fully data-driven method to estimate a lower bound for the structured singular value, by conducting experiments on the system and applying power iterations to the collected data. Our numerical simulations demonstrate that this method effectively lower bounds the structured singular value, yielding results comparable to the MATLAB$^©$ Robust Control Toolbox. |
| title | Data-Driven Estimation of Structured Singular Values |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2503.13410 |