A differential geometric setting for dynamic equivalence and dynamic linearization

Jean-Baptiste Pomet

Banach Center Publications (1995)

  • Volume: 32, Issue: 1, page 319-339
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Pomet, Jean-Baptiste. "A differential geometric setting for dynamic equivalence and dynamic linearization." Banach Center Publications 32.1 (1995): 319-339. <http://eudml.org/doc/262861>.

@article{Pomet1995,
abstract = {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.},
author = {Pomet, Jean-Baptiste},
journal = {Banach Center Publications},
keywords = {flat systems; infinite jet bundles; Dynamic feedback equivalence; dynamic feedback linearization; Lie-Bäcklund transformations; contact transformations; dynamic linearization; dynamic equivalence},
language = {eng},
number = {1},
pages = {319-339},
title = {A differential geometric setting for dynamic equivalence and dynamic linearization},
url = {http://eudml.org/doc/262861},
volume = {32},
year = {1995},
}

TY - JOUR
AU - Pomet, Jean-Baptiste
TI - A differential geometric setting for dynamic equivalence and dynamic linearization
JO - Banach Center Publications
PY - 1995
VL - 32
IS - 1
SP - 319
EP - 339
AB - 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.
LA - eng
KW - flat systems; infinite jet bundles; Dynamic feedback equivalence; dynamic feedback linearization; Lie-Bäcklund transformations; contact transformations; dynamic linearization; dynamic equivalence
UR - http://eudml.org/doc/262861
ER -

References

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Citations in EuDML Documents

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  1. Jean-Baptiste Pomet, On dynamic feedback linearization of four-dimensional affine control systems with two inputs
  2. E. Aranda-Bricaire, C. Moog, J. Pomet, Infinitesimal Brunovský form for nonlinear systems with applications to Dynamic Linearization
  3. Michel Fliess, Jean Lévine, Philippe Martin, Pierre Rouchon, Differential flatness and defect: an overview
  4. David Avanessoff, Jean-Baptiste Pomet, Flatness and Monge parameterization of two-input systems, control-affine with 4 states or general with 3 states
  5. Shun-Jie Li, Witold Respondek, Flat outputs of two-input driftless control systems
  6. Shun-Jie Li, Witold Respondek, Flat outputs of two-input driftless control systems
  7. Shun-Jie Li, Witold Respondek, Flat outputs of two-input driftless control systems

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