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, Volume 13 (2007) no. 2, p. 237-264

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 “$\left(x,u\right)$-flatness” of these systems, with much more elementary techniques.

DOI : https://doi.org/10.1051/cocv:2007011
Classification:  93B18,  93B29,  34C20
Keywords: dynamic feedback linearization, flat control systems, Monge problem, Monge equations
@article{COCV_2007__13_2_237_0,
author = {Avanessoff, David and Pomet, Jean-Baptiste},
title = {Flatness and Monge parameterization of two-input systems, control-affine with 4 states or general with 3 states},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {13},
number = {2},
year = {2007},
pages = {237-264},
doi = {10.1051/cocv:2007011},
zbl = {pre05173183},
mrnumber = {2306635},
language = {en},
url = {http://www.numdam.org/item/COCV_2007__13_2_237_0}
}

Avanessoff, David; 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, Volume 13 (2007) no. 2, pp. 237-264. doi : 10.1051/cocv:2007011. http://www.numdam.org/item/COCV_2007__13_2_237_0/

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