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 “-flatness” of these systems, with much more elementary techniques.
Mots clés : 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}, pages = {237--264}, publisher = {EDP-Sciences}, volume = {13}, number = {2}, year = {2007}, doi = {10.1051/cocv:2007011}, mrnumber = {2306635}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv:2007011/} }
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 PY - 2007 SP - 237 EP - 264 VL - 13 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2007011/ DO - 10.1051/cocv:2007011 LA - en ID - COCV_2007__13_2_237_0 ER -
%0 Journal Article %A Avanessoff, David %A Pomet, Jean-Baptiste %T Flatness and Monge parameterization of two-input systems, control-affine with 4 states or general with 3 states %J ESAIM: Control, Optimisation and Calculus of Variations %D 2007 %P 237-264 %V 13 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2007011/ %R 10.1051/cocv:2007011 %G en %F 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, Tome 13 (2007) no. 2, pp. 237-264. doi : 10.1051/cocv:2007011. http://www.numdam.org/articles/10.1051/cocv:2007011/
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