Issues with Input-Space Representation in Nonlinear Data-Based Dissipativity Estimation
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916489373679616 |
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| author | LoCicero, Ethan Penne, Alex Bridgeman, Leila |
| author_facet | LoCicero, Ethan Penne, Alex Bridgeman, Leila |
| contents | In data-based control, dissipativity can be a powerful tool for attaining stability guarantees for nonlinear systems if that dissipativity can be inferred from data. This work provides a tutorial on several existing methods for data-based dissipativity estimation of nonlinear systems. The interplay between the underlying assumptions of these methods and their sample complexity is investigated. It is shown that methods based on delta-covering result in an intractable trade-off between sample complexity and robustness. A new method is proposed to quantify the robustness of machine learning-based dissipativity estimation. It is shown that this method achieves a more tractable trade-off between robustness and sample complexity. Several numerical case studies demonstrate the results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13404 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Issues with Input-Space Representation in Nonlinear Data-Based Dissipativity Estimation LoCicero, Ethan Penne, Alex Bridgeman, Leila Systems and Control Optimization and Control In data-based control, dissipativity can be a powerful tool for attaining stability guarantees for nonlinear systems if that dissipativity can be inferred from data. This work provides a tutorial on several existing methods for data-based dissipativity estimation of nonlinear systems. The interplay between the underlying assumptions of these methods and their sample complexity is investigated. It is shown that methods based on delta-covering result in an intractable trade-off between sample complexity and robustness. A new method is proposed to quantify the robustness of machine learning-based dissipativity estimation. It is shown that this method achieves a more tractable trade-off between robustness and sample complexity. Several numerical case studies demonstrate the results. |
| title | Issues with Input-Space Representation in Nonlinear Data-Based Dissipativity Estimation |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2411.13404 |