| dc.contributor | Springer | |
| dc.creator | Lizárraga Navarro, David Antonio | |
| dc.date | 2018-06-07T20:16:50Z | |
| dc.date | 2018-06-07T20:16:50Z | |
| dc.date | 2011-12 | |
| dc.date.accessioned | 2023-07-17T22:03:09Z | |
| dc.date.available | 2023-07-17T22:03:09Z | |
| dc.identifier | Lizárraga, D.A. Math. Control Signals Syst. (2011) 23: 177. https://doi.org/10.1007/s00498-011-0067-6 | |
| dc.identifier | http://hdl.handle.net/11627/3868 | |
| dc.identifier | https://doi.org/10.1007/s00498-011-0067-6 | |
| dc.identifier.uri | https://repositorioslatinoamericanos.uchile.cl/handle/2250/7543393 | |
| dc.description | "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)." | |
| dc.format | application/pdf | |
| dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | |
| dc.rights | http://creativecommons.org/licenses/by-nc-nd/4.0/ | |
| dc.rights | Acceso Abierto | |
| dc.subject | Transversality | |
| dc.subject | Transverse function approach | |
| dc.subject | Weak and strong topologies | |
| dc.subject | Control of nonholonomic systems | |
| dc.subject | MATEMÁTICAS | |
| dc.title | On the transversality of functions at the core of the transverse function approach to control | |
| dc.type | article | |
