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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| Date: | 2009 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2009
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149099 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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| Summary: | 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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