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Flat outputs of two-input driftless control systems

Published online by Cambridge University Press:  14 October 2011

Shun-Jie Li  and
Witold Respondek
Shun-Jie Li
Affiliation:
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
Witold Respondek
Affiliation:
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
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Abstract

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.

Keywords

Control systemflatnessflat outputfeedback equivalencecharacteristic distributionn-trailer system
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 18 , Issue 3 , July 2012 , pp. 774 - 798
Copyright
© EDP Sciences, SMAI, 2011

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