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We study the problem of flatness of two-input driftless control systems. Although a characterization of flat systems of that class is known, the problems of describing all flat outputs and of calculating them is open and we solve it in the paper. We show that all x-flat outputs are parameterized by an arbitrary function of three canonically defined variables. We also construct a system of 1st order PDE's whose solutions give all x-flat outputs of two-input driftless systems. We illustrate our results by describing all x-flat outputs of models of a nonholonomic car and the n-trailer system.
@article{COCV_2012__18_3_774_0,
author = {Li, Shun-Jie and Respondek, Witold},
title = {Flat outputs of two-input driftless control systems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {774--798},
publisher = {EDP-Sciences},
volume = {18},
number = {3},
year = {2012},
doi = {10.1051/cocv/2011181},
mrnumber = {3041664},
zbl = {1252.93041},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2011181/}
}
TY - JOUR AU - Li, Shun-Jie AU - Respondek, Witold TI - Flat outputs of two-input driftless control systems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2012 SP - 774 EP - 798 VL - 18 IS - 3 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2011181/ DO - 10.1051/cocv/2011181 LA - en ID - COCV_2012__18_3_774_0 ER -
%0 Journal Article %A Li, Shun-Jie %A Respondek, Witold %T Flat outputs of two-input driftless control systems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2012 %P 774-798 %V 18 %N 3 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2011181/ %R 10.1051/cocv/2011181 %G en %F COCV_2012__18_3_774_0
Li, Shun-Jie; Respondek, Witold. Flat outputs of two-input driftless control systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 3, pp. 774-798. doi: 10.1051/cocv/2011181
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