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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2412.17384 |
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| _version_ | 1866909767537000448 |
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| author | Gherdaoui, Théo |
| author_facet | Gherdaoui, Théo |
| contents | We present a necessary condition for the small-time local controllability of multi-input control-affine systems on $R^d$ . This condition is formulated on the vectors of $R^d$ resulting from the evaluation at zero of the Lie brackets of the vector fields: it involves both their direction and their amplitude. The proof is an adaptation to the multi-input case of a general method introduced by Beauchard and Marbach in the single-input case. It relies on a Magnus-type representation formula: the state is approximated by a linear combination of the evaluation at zero of the Lie brackets of the vector fields, whose coefficients are functionals of the time and the controls. Finally, obstructions to small-time local controllability result from interpolation inequalities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17384 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quadratic obstructions to small-time local controllability for multi-input systems Gherdaoui, Théo Optimization and Control We present a necessary condition for the small-time local controllability of multi-input control-affine systems on $R^d$ . This condition is formulated on the vectors of $R^d$ resulting from the evaluation at zero of the Lie brackets of the vector fields: it involves both their direction and their amplitude. The proof is an adaptation to the multi-input case of a general method introduced by Beauchard and Marbach in the single-input case. It relies on a Magnus-type representation formula: the state is approximated by a linear combination of the evaluation at zero of the Lie brackets of the vector fields, whose coefficients are functionals of the time and the controls. Finally, obstructions to small-time local controllability result from interpolation inequalities. |
| title | Quadratic obstructions to small-time local controllability for multi-input systems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2412.17384 |