caa a22 4500 44586852X CHVBK 20180317145505.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00498-011-0067-6 doi (NATIONALLICENCE)springer-10.1007/s00498-011-0067-6 Lizárraga David División de Matemáticas Aplicadas, IPICYT, Camino a la Presa San José 2055, Col. Lomas 4a sección, CP 78216, San Luis Potosí, SLP, Mexico aut On the transversality of functions at the core of the transverse function approach to control [Elektronische Daten] [David Lizárraga] 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 $${f : M \longrightarrow Q}$$ 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 ∞-”) topology on C ∞(M, Q). Springer-Verlag London Limited, 2011 Transversality nationallicence Transverse function approach nationallicence Weak and strong topologies nationallicence Control of nonholonomic systems nationallicence Mathematics of Control, Signals, and Systems Springer-Verlag 23/1-3(2011-12-01), 177-197 0932-4194 23:1-3<177 2011 23 498 https://doi.org/10.1007/s00498-011-0067-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00498-011-0067-6 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Lizárraga David División de Matemáticas Aplicadas, IPICYT, Camino a la Presa San José 2055, Col. Lomas 4a sección, CP 78216, San Luis Potosí, SLP, Mexico aut NATIONALLICENCE 773 0- Mathematics of Control, Signals, and Systems Springer-Verlag 23/1-3(2011-12-01), 177-197 0932-4194 23:1-3<177 2011 23 498 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer