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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.06446 |
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| _version_ | 1866918087031259136 |
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| author | Uzeda, Erick Mejia Broucke, Mireille E. |
| author_facet | Uzeda, Erick Mejia Broucke, Mireille E. |
| contents | This paper addresses a shortcoming in adaptive control, that the property of a regressor being persistently exciting (PE) is not well-behaved. One can construct regressors that upend the commonsense notion that excitation should not be created out of nothing. To amend the situation, a notion of regularity of regressors is needed. We are naturally led to a broad class of regular regressors that enjoy the property that their excitation is always confined to a subspace, a foundational result called the PE decomposition. A geometric characterization of regressor excitation opens up new avenues for adaptive control, as we demonstrate by formulating a number of new adaptive control problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06446 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Regular Regressors in Adaptive Control Uzeda, Erick Mejia Broucke, Mireille E. Systems and Control 93C40 (Primary), 93B27 (Secondary) This paper addresses a shortcoming in adaptive control, that the property of a regressor being persistently exciting (PE) is not well-behaved. One can construct regressors that upend the commonsense notion that excitation should not be created out of nothing. To amend the situation, a notion of regularity of regressors is needed. We are naturally led to a broad class of regular regressors that enjoy the property that their excitation is always confined to a subspace, a foundational result called the PE decomposition. A geometric characterization of regressor excitation opens up new avenues for adaptive control, as we demonstrate by formulating a number of new adaptive control problems. |
| title | On Regular Regressors in Adaptive Control |
| topic | Systems and Control 93C40 (Primary), 93B27 (Secondary) |
| url | https://arxiv.org/abs/2507.06446 |