A new perspective on Willems' fundamental lemma: Universality of persistently exciting inputs
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916781608665088 |
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| author | Shakouri, Amir van Waarde, Henk J. Camlibel, M. Kanat |
| author_facet | Shakouri, Amir van Waarde, Henk J. Camlibel, M. Kanat |
| contents | In this letter, we provide new insight into Willems et al.'s fundamental lemma by studying the concept of universal inputs. An input is called universal if, when applied to any controllable system, it leads to input-output data that parametrizes all finite trajectories of the system. By the fundamental lemma, inputs that are persistently exciting of sufficiently high order are universal. The main contribution of this work is to prove the converse. Therefore, universality and persistency of excitation are equivalent. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_12489 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A new perspective on Willems' fundamental lemma: Universality of persistently exciting inputs Shakouri, Amir van Waarde, Henk J. Camlibel, M. Kanat Optimization and Control In this letter, we provide new insight into Willems et al.'s fundamental lemma by studying the concept of universal inputs. An input is called universal if, when applied to any controllable system, it leads to input-output data that parametrizes all finite trajectories of the system. By the fundamental lemma, inputs that are persistently exciting of sufficiently high order are universal. The main contribution of this work is to prove the converse. Therefore, universality and persistency of excitation are equivalent. |
| title | A new perspective on Willems' fundamental lemma: Universality of persistently exciting inputs |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2503.12489 |