dc.contributor
Universitat Politècnica de Catalunya. Departament de Matemàtiques
dc.contributor
Universitat Politècnica de Catalunya. CRG - Grup de Robòtica Computacional
dc.contributor.author
Franch Bullich, Jaume
dc.contributor.author
Lévine, Jean
dc.date.accessioned
2026-02-14T03:23:09Z
dc.date.available
2026-02-14T03:23:09Z
dc.date.issued
2025-11-22
dc.identifier
Franch, J.; Lévine, J. On driftless systems with m controls and 2m or 2m - 1 states that are flat by pure prolongation. «Geometric Mechanics», 22 Novembre 2025,
dc.identifier
https://hdl.handle.net/2117/455216
dc.identifier
10.1142/S297245892540012X
dc.identifier.uri
http://hdl.handle.net/2117/455216
dc.description.abstract
It is widely recognized that no tractable necessary and sufficient conditions exist for determining whether a system is, in general, differentially flat. However, specific cases do provide such conditions. For instance, driftless systems with two inputs have known necessary and sufficient conditions. For driftless systems with three or more inputs, the available conditions are only sufficient. This paper presents new findings on determining whether a system with [Formula: see text] inputs and [Formula: see text] or [Formula: see text] states is flat by pure prolongation, a specific subclass of differential flatness. While this condition is more restrictive than general differential flatness, the algorithm for computing flat outputs remains remarkably simple, and the verification requirements are relatively lenient. Moreover, the conditions proposed in this work broaden the class of systems recognized as differentially flat, as our sufficient condition differs from existing criteria.
dc.description.abstract
Peer Reviewed
dc.description.abstract
Postprint (author's final draft)
dc.format
application/pdf
dc.relation
https://www.worldscientific.com/worldscinet/gm
dc.rights
http://creativecommons.org/licenses/by/4.0/
dc.rights
Attribution 4.0 International
dc.subject
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa
dc.subject
Nonlinear control systems
dc.subject
differential geometric control
dc.subject
driftless system
dc.subject
differential flatness
dc.subject
pure prolongation
dc.subject
Sistemes de control
dc.subject
Classificació AMS::93 Systems Theory; Control::93C Control systems, guided systems
dc.title
On driftless systems with m controls and 2m or 2m - 1 states that are flat by pure prolongation
