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Geometry of Optimal Control for Control-Affine Systems
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2013, том 9
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Geometry of Optimal Control for Control-Affine Systems
Інший ID:
2010 Mathematics Subject Classification: 58A30; 53C17; 58A15; 53C10
DOI: http://dx.doi.org/10.3842/SIGMA.2013.034
DOI: http://dx.doi.org/10.3842/SIGMA.2013.034
Посилання:
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.
Підтримка:
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.
Дата:
2013
Переглядів:
553
Завантажень:
235
Анотація:
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.
