An accessibility condition for discrete-time linear systems on Lie groups
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911930435764224 |
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| author | Cavalheiro, Thiago Matheus Santana, Alexandre José Viscovini, Eduardo Celso |
| author_facet | Cavalheiro, Thiago Matheus Santana, Alexandre José Viscovini, Eduardo Celso |
| contents | In this paper, we characterize the accessibility of discrete-time linear control systems on Lie groups. Using an exceptional notion of derivative, we construct a subalgebra $\mathfrak{h}$ based on the infinitesimal automorphism of the system such that if its dimension is maximal, the system is accessible. Our criteria provide simple conditions in a general context for the discrete-time case. Additionally, we prove a sufficient condition for local controllability at the identity using the infinitesimal automorphism, akin to the ad-rank condition in the continuous case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16237 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An accessibility condition for discrete-time linear systems on Lie groups Cavalheiro, Thiago Matheus Santana, Alexandre José Viscovini, Eduardo Celso Optimization and Control In this paper, we characterize the accessibility of discrete-time linear control systems on Lie groups. Using an exceptional notion of derivative, we construct a subalgebra $\mathfrak{h}$ based on the infinitesimal automorphism of the system such that if its dimension is maximal, the system is accessible. Our criteria provide simple conditions in a general context for the discrete-time case. Additionally, we prove a sufficient condition for local controllability at the identity using the infinitesimal automorphism, akin to the ad-rank condition in the continuous case. |
| title | An accessibility condition for discrete-time linear systems on Lie groups |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2406.16237 |