This paper presents an (infinite-dimensional) geometric framework for control systems, based on infinite jet bundles, where a system is represented by a single vector field and dynamic equivalence (to be precise: equivalence by endogenous dynamic feedback) is conjugation by diffeomorphisms. These diffeomorphisms are very much related to Lie-Bäcklund transformations. It is proved in this framework that dynamic equivalence of single-input systems is the same as static equivalence.
@article{bwmeta1.element.bwnjournal-article-bcpv32z1p319bwm,
author = {Pomet, Jean-Baptiste},
title = {A differential geometric setting for dynamic equivalence and dynamic linearization},
journal = {Banach Center Publications},
volume = {31},
year = {1995},
pages = {319-339},
zbl = {0838.93019},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv32z1p319bwm}
}
Pomet, Jean-Baptiste. A differential geometric setting for dynamic equivalence and dynamic linearization. Banach Center Publications, Tome 31 (1995) pp. 319-339. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv32z1p319bwm/
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