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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.05863 |
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| _version_ | 1866912301425098752 |
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| author | Aldana-Lopez, Rodrigo Seeber, Richard Haimovich, Hernan Gomez-Gutierrez, David |
| author_facet | Aldana-Lopez, Rodrigo Seeber, Richard Haimovich, Hernan Gomez-Gutierrez, David |
| contents | The signal differentiation problem involves the development of algorithms that allow to recover a signal's derivatives from noisy measurements. This paper develops a first-order differentiator with the following combination of properties: robustness to measurement noise, exactness in the absence of noise, optimal worst-case differentiation error, and Lipschitz continuous output where the output's Lipschitz constant is a tunable parameter. This combination of advantageous properties is not shared by any existing differentiator. Both continuous-time and sample-based versions of the differentiator are developed and theoretical guarantees are established for both. The continuous-time version of the differentiator consists in a regularized and sliding-mode-filtered linear adaptive differentiator. The sample-based, implementable version is then obtained through appropriate discretization. An illustrative example is provided to highlight the features of the developed differentiator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05863 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal robust exact first-order differentiators with Lipschitz continuous output Aldana-Lopez, Rodrigo Seeber, Richard Haimovich, Hernan Gomez-Gutierrez, David Systems and Control The signal differentiation problem involves the development of algorithms that allow to recover a signal's derivatives from noisy measurements. This paper develops a first-order differentiator with the following combination of properties: robustness to measurement noise, exactness in the absence of noise, optimal worst-case differentiation error, and Lipschitz continuous output where the output's Lipschitz constant is a tunable parameter. This combination of advantageous properties is not shared by any existing differentiator. Both continuous-time and sample-based versions of the differentiator are developed and theoretical guarantees are established for both. The continuous-time version of the differentiator consists in a regularized and sliding-mode-filtered linear adaptive differentiator. The sample-based, implementable version is then obtained through appropriate discretization. An illustrative example is provided to highlight the features of the developed differentiator. |
| title | Optimal robust exact first-order differentiators with Lipschitz continuous output |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2404.05863 |