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.
Publié le : 1995-07-04
Classification:
Nonlinear control systems,
Dynamic feedback equivalence,
Dynamic feedback linearization,
Endogenous dynamic feedback,
Infinite jet bundles,
Pfaffian systems,
Linearized control system.,
Contact transformations,
Brunovsky canonical form,
Flat systems,
Lie-Bäcklund transformations,
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
@article{hal-01501078,
author = {Pomet, Jean-Baptiste},
title = {A differential geometric setting for dynamic equivalence and dynamic linearization},
journal = {HAL},
volume = {1995},
number = {0},
year = {1995},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-01501078}
}
Pomet, Jean-Baptiste. A differential geometric setting for dynamic equivalence and dynamic linearization. HAL, Tome 1995 (1995) no. 0, . http://gdmltest.u-ga.fr/item/hal-01501078/