Optimal Trajectory Control of Geometrically Exact Strings with Space-Time Finite Elements
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910792008335360 |
|---|---|
| author | Thoma, Tobias Kotyczka, Paul |
| author_facet | Thoma, Tobias Kotyczka, Paul |
| contents | In this contribution, we present a variational space-time formulation which generates an optimal feed-forward controller for geometrically exact strings. More concretely, the optimization problem is solved with an indirect approach, and the space-time finite element method translates the problem to a set of algebraic equations. Thereby, only the positional field and the corresponding adjoint variable field are approximated by continuous shape functions, which makes the discretization of a velocity field unnecessary. In addition, the variational formulation can be solved using commercial or open source finite element packages. The entire approach can also be interpreted as a multiple-shooting method for solving the optimality conditions based on the semi-discrete problem. The performance of our approach is demonstrated by a numerical test. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11522 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Trajectory Control of Geometrically Exact Strings with Space-Time Finite Elements Thoma, Tobias Kotyczka, Paul Systems and Control In this contribution, we present a variational space-time formulation which generates an optimal feed-forward controller for geometrically exact strings. More concretely, the optimization problem is solved with an indirect approach, and the space-time finite element method translates the problem to a set of algebraic equations. Thereby, only the positional field and the corresponding adjoint variable field are approximated by continuous shape functions, which makes the discretization of a velocity field unnecessary. In addition, the variational formulation can be solved using commercial or open source finite element packages. The entire approach can also be interpreted as a multiple-shooting method for solving the optimality conditions based on the semi-discrete problem. The performance of our approach is demonstrated by a numerical test. |
| title | Optimal Trajectory Control of Geometrically Exact Strings with Space-Time Finite Elements |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2501.11522 |