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http://ipicyt.repositorioinstitucional.mx/jspui/handle/1010/1496| On the transversality of functions at the core of the transverse function approach to control | |
| DAVID ANTONIO LIZARRAGA NAVARRO | |
| Acceso Abierto | |
| Atribución-NoComercial-SinDerivadas | |
| https://doi.org/10.1007/s00498-011-0067-6 | |
| Transversality Transverse function approach Weak and strong topologies Control of nonholonomic systems | |
| "The transverse function approach to control, introduced by Morin and Samson in the early 2000s, is based on functions that are transverse to a set of vector fields in a sense formally similar to, although strictly speaking different from, the classical notion of transversality in differential topology. In this paper, a precise link is established between transversality and the functions used in the transverse function approach. It is first shown that a smooth function f : M -> Q is transverse to a set of vector fields which locally span a distribution D on Q if, and only if, its tangent mapping T f is transverse to D, where D is regarded as a submanifold of the tangent bundle T Q. It is further shown that each of these two conditions is equivalent to transversality of T f to D along the zero section of T M. These results are then used to rigorously state and prove that if M is compact and D is a distribution on Q, then the set of mappings of M into Q that are transverse to D is open in the strong (or "Whitney C (a)-") topology on C (a)(M, Q)." | |
| Springer | |
| 2011-12 | |
| Artículo | |
| Lizárraga, D.A. Math. Control Signals Syst. (2011) 23: 177. https://doi.org/10.1007/s00498-011-0067-6 | |
| MATEMÁTICAS | |
| Versión aceptada | |
| acceptedVersion - Versión aceptada | |
| Aparece en las colecciones: | Publicaciones Científicas Control y Sistemas Dinámicos |
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