| Issue |
ESAIM: COCV
Volume 18, Number 3, July-September 2012
|
|
|---|---|---|
| Page(s) | 774 - 798 | |
| DOI | https://doi.org/10.1051/cocv/2011181 | |
| Published online | 14 October 2011 | |
Flat outputs of two-input driftless control systems
INSA-Rouen, Laboratoire de Mathématiques, Avenue de
l’Université, 76801
Saint-Etienne-du-Rouvray,
France
shunjie.li@insa-rouen.fr; witold.respondek@insa-rouen.fr
Received:
18
November
2010
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.
Mathematics Subject Classification: 93B27 / 93C10 / 93C95
Key words: Control system / flatness / flat output / feedback equivalence / characteristic distribution / n-trailer system
© EDP Sciences, SMAI, 2011
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