Flatness and Monge parameterization of two-input systems, control-affine with 4 states or general with 3 states

David Avanessoff; Jean-Baptiste Pomet

ESAIM: Control, Optimisation and Calculus of Variations (2007)

  • Volume: 13, Issue: 2, page 237-264
  • ISSN: 1292-8119

Abstract

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This paper studies Monge parameterization, or differential flatness, of control-affine systems with four states and two controls. Some of them are known to be flat, and this implies admitting a Monge parameterization. Focusing on systems outside this class, we describe the only possible structure of such a parameterization for these systems, and give a lower bound on the order of this parameterization, if it exists. This lower-bound is good enough to recover the known results about “(x,u)-flatness” of these systems, with much more elementary techniques.

How to cite

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Avanessoff, David, and Pomet, Jean-Baptiste. "Flatness and Monge parameterization of two-input systems, control-affine with 4 states or general with 3 states." ESAIM: Control, Optimisation and Calculus of Variations 13.2 (2007): 237-264. <http://eudml.org/doc/250034>.

@article{Avanessoff2007,
abstract = { This paper studies Monge parameterization, or differential flatness, of control-affine systems with four states and two controls. Some of them are known to be flat, and this implies admitting a Monge parameterization. Focusing on systems outside this class, we describe the only possible structure of such a parameterization for these systems, and give a lower bound on the order of this parameterization, if it exists. This lower-bound is good enough to recover the known results about “(x,u)-flatness” of these systems, with much more elementary techniques. },
author = {Avanessoff, David, Pomet, Jean-Baptiste},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Dynamic feedback linearization; flat control systems; Monge problem; Monge equations; Monge problem},
language = {eng},
month = {5},
number = {2},
pages = {237-264},
publisher = {EDP Sciences},
title = {Flatness and Monge parameterization of two-input systems, control-affine with 4 states or general with 3 states},
url = {http://eudml.org/doc/250034},
volume = {13},
year = {2007},
}

TY - JOUR
AU - Avanessoff, David
AU - Pomet, Jean-Baptiste
TI - Flatness and Monge parameterization of two-input systems, control-affine with 4 states or general with 3 states
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2007/5//
PB - EDP Sciences
VL - 13
IS - 2
SP - 237
EP - 264
AB - This paper studies Monge parameterization, or differential flatness, of control-affine systems with four states and two controls. Some of them are known to be flat, and this implies admitting a Monge parameterization. Focusing on systems outside this class, we describe the only possible structure of such a parameterization for these systems, and give a lower bound on the order of this parameterization, if it exists. This lower-bound is good enough to recover the known results about “(x,u)-flatness” of these systems, with much more elementary techniques.
LA - eng
KW - Dynamic feedback linearization; flat control systems; Monge problem; Monge equations; Monge problem
UR - http://eudml.org/doc/250034
ER -

References

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