Geometry of Optimal Control for Control-Affine Systems
Motivated by the ubiquity of control-affine systems in optimal control theory, we investigate the geometry of point-affine control systems with metric structures in dimensions two and three. We compute local isometric invariants for point-affine distributions of constant type with metric structures...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2013 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2013
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149206 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Geometry of Optimal Control for Control-Affine Systems / J.N. Clelland, C.G. Moseley, G.R. Wilkens // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 6 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862700143996829696 |
|---|---|
| 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 Optimal Control for Control-Affine Systems / J.N. Clelland, C.G. Moseley, G.R. Wilkens // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 6 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Motivated by the ubiquity of control-affine systems in optimal control theory, we investigate the geometry of point-affine control systems with metric structures in dimensions two and three. We compute local isometric invariants for point-affine distributions of constant type with metric structures for systems with 2 states and 1 control and systems with 3 states and 1 control, and use Pontryagin's maximum principle to find geodesic trajectories for homogeneous examples. Even in these low dimensions, the behavior of these systems is surprisingly rich and varied.
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| first_indexed | 2025-12-07T16:37:57Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149206 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T16:37:57Z |
| publishDate | 2013 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Clelland, J.N. Moseley, C.G. Wilkens, G.R. 2019-02-19T18:35:52Z 2019-02-19T18:35:52Z 2013 Geometry of Optimal Control for Control-Affine Systems / J.N. Clelland, C.G. Moseley, G.R. Wilkens // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 6 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 58A30; 53C17; 58A15; 53C10 DOI: http://dx.doi.org/10.3842/SIGMA.2013.034 https://nasplib.isofts.kiev.ua/handle/123456789/149206 Motivated by the ubiquity of control-affine systems in optimal control theory, we investigate the geometry of point-affine control systems with metric structures in dimensions two and three. We compute local isometric invariants for point-affine distributions of constant type with metric structures for systems with 2 states and 1 control and systems with 3 states and 1 control, and use Pontryagin's maximum principle to find geodesic trajectories for homogeneous examples. Even in these low dimensions, the behavior of these systems is surprisingly rich and varied. This research was supported in part by NSF grants DMS-0908456 and DMS-1206272. We
 would like to thank the referees for many helpful suggestions, which significantly improved the
 organization and exposition of this paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Geometry of Optimal Control for Control-Affine Systems Article published earlier |
| spellingShingle | Geometry of Optimal Control for Control-Affine Systems Clelland, J.N. Moseley, C.G. Wilkens, G.R. |
| title | Geometry of Optimal Control for Control-Affine Systems |
| title_full | Geometry of Optimal Control for Control-Affine Systems |
| title_fullStr | Geometry of Optimal Control for Control-Affine Systems |
| title_full_unstemmed | Geometry of Optimal Control for Control-Affine Systems |
| title_short | Geometry of Optimal Control for Control-Affine Systems |
| title_sort | geometry of optimal control for control-affine systems |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149206 |
| work_keys_str_mv | AT clellandjn geometryofoptimalcontrolforcontrolaffinesystems AT moseleycg geometryofoptimalcontrolforcontrolaffinesystems AT wilkensgr geometryofoptimalcontrolforcontrolaffinesystems |