# 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

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topAvanessoff, 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 -

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