A Dual Geometric Test for Forward-Flatness
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912515324116992 |
|---|---|
| author | Kolar, Bernd Schrotshamer, Johannes Schöberl, Markus |
| author_facet | Kolar, Bernd Schrotshamer, Johannes Schöberl, Markus |
| contents | Forward-flatness is a generalization of static feedback linearizability and a special case of a more general flatness concept for discrete-time systems. Recently, it has been shown that this practically quite relevant property can be checked by computing a unique sequence of involutive distributions which generalizes the well-known static feedback linearization test. In this paper, a dual test for forward-flatness based on a unique sequence of integrable codistributions is derived. Since the main mathematical operations for determining this sequence are the intersection of codistributions and the calculation of Lie derivatives of 1-forms, it is computationally quite efficient. Furthermore, the formulation with codistributions also facilitates a comparison with the existing discrete-time literature regarding the closely related topic of dynamic feedback linearization, which is mostly formulated in terms of 1-forms rather than vector fields. The presented results are illustrated by two examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02816 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Dual Geometric Test for Forward-Flatness Kolar, Bernd Schrotshamer, Johannes Schöberl, Markus Optimization and Control Differential Geometry Dynamical Systems Forward-flatness is a generalization of static feedback linearizability and a special case of a more general flatness concept for discrete-time systems. Recently, it has been shown that this practically quite relevant property can be checked by computing a unique sequence of involutive distributions which generalizes the well-known static feedback linearization test. In this paper, a dual test for forward-flatness based on a unique sequence of integrable codistributions is derived. Since the main mathematical operations for determining this sequence are the intersection of codistributions and the calculation of Lie derivatives of 1-forms, it is computationally quite efficient. Furthermore, the formulation with codistributions also facilitates a comparison with the existing discrete-time literature regarding the closely related topic of dynamic feedback linearization, which is mostly formulated in terms of 1-forms rather than vector fields. The presented results are illustrated by two examples. |
| title | A Dual Geometric Test for Forward-Flatness |
| topic | Optimization and Control Differential Geometry Dynamical Systems |
| url | https://arxiv.org/abs/2404.02816 |