A differential geometric setting for dynamic equivalence and dynamic linearization

Jean-Baptiste Pomet 1
1 McTAO - Mathematics for Control, Transport and Applications
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : This paper presents an (infinite dimensional) geometric framework for control system, 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. NB: this paper is followed by "Infinitesimal Brunovsky form for nonlinear systems with applications to dynamic linearization", by E. Aranda-Bricaire, C. H. Moog and J.-B. Pomet, published in the same 1995 volume, which is its natural follow-up. This is a corrected version of the reports http://hal.inria.fr/inria-00074360 and http://hal.inria.fr/inria-00074361.
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  • is format of inria-00074361 - That "rapport de recherche" was a preliminary version. The present document is a slightly enriched version of the published article.

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Jean-Baptiste Pomet. A differential geometric setting for dynamic equivalence and dynamic linearization. Banach Center Publications, Institute of Mathematics Polish Academy of Sciences, 1995, 32, pp.319 - 339. ⟨https://eudml.org/doc/262861⟩. ⟨10.4064/-32-1-319-339⟩. ⟨hal-01501078⟩

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