Geometry of Control-Affine Systems
Motivated by control-affine systems in optimal control theory, we introduce the notion of a point-affine distribution on a manifold X – i.e., an affine distribution F together with a distinguished vector field contained in F. We compute local invariants for point-affine distributions of constant typ...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2009 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2009
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149099 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Geometry of Control-Affine Systems / J.N. Clelland, C.G. Moseley, G.R. Wilkens // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 26 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862570991037710336 |
|---|---|
| author | Clelland, J.N. Moseley, C.G. Wilkens, G.R. |
| author_facet | Clelland, J.N. Moseley, C.G. Wilkens, G.R. |
| citation_txt | Geometry of Control-Affine Systems / J.N. Clelland, C.G. Moseley, G.R. Wilkens // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 26 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Motivated by control-affine systems in optimal control theory, we introduce the notion of a point-affine distribution on a manifold X – i.e., an affine distribution F together with a distinguished vector field contained in F. We compute local invariants for point-affine distributions of constant type when dim(X) = n, rank(F) = n–1, and when dim(X) = 3, rank(F) = 1. Unlike linear distributions, which are characterized by integer-valued invariants – namely, the rank and growth vector – when dim(X) ≤ 4, we find local invariants depending on arbitrary functions even for rank 1 point-affine distributions on manifolds of dimension 2.
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| first_indexed | 2025-11-26T03:21:34Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149099 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-26T03:21:34Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Clelland, J.N. Moseley, C.G. Wilkens, G.R. 2019-02-19T17:20:18Z 2019-02-19T17:20:18Z 2009 Geometry of Control-Affine Systems / J.N. Clelland, C.G. Moseley, G.R. Wilkens // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 26 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 58A30; 53C17; 58A15; 53C10 https://nasplib.isofts.kiev.ua/handle/123456789/149099 Motivated by control-affine systems in optimal control theory, we introduce the notion of a point-affine distribution on a manifold X – i.e., an affine distribution F together with a distinguished vector field contained in F. We compute local invariants for point-affine distributions of constant type when dim(X) = n, rank(F) = n–1, and when dim(X) = 3, rank(F) = 1. Unlike linear distributions, which are characterized by integer-valued invariants – namely, the rank and growth vector – when dim(X) ≤ 4, we find local invariants depending on arbitrary functions even for rank 1 point-affine distributions on manifolds of dimension 2. This paper is a contribution to the Special Issue “Elie Cartan and Differential Geometry”. This work was partially supported by NSF grant DMS-0908456. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Geometry of Control-Affine Systems Article published earlier |
| spellingShingle | Geometry of Control-Affine Systems Clelland, J.N. Moseley, C.G. Wilkens, G.R. |
| title | Geometry of Control-Affine Systems |
| title_full | Geometry of Control-Affine Systems |
| title_fullStr | Geometry of Control-Affine Systems |
| title_full_unstemmed | Geometry of Control-Affine Systems |
| title_short | Geometry of Control-Affine Systems |
| title_sort | geometry of control-affine systems |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149099 |
| work_keys_str_mv | AT clellandjn geometryofcontrolaffinesystems AT moseleycg geometryofcontrolaffinesystems AT wilkensgr geometryofcontrolaffinesystems |