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Flatness and Monge parameterization of two-input systems,control-affine with 4 states or general with 3 states

Published online by Cambridge University Press:  12 May 2007

David Avanessoff  and
Jean-Baptiste Pomet
David Avanessoff
Affiliation:
INRIA Sophia Antipolis, B.P. 93, 06902 Sophia Antipolis cedex, France; [email protected]; [email protected]
Jean-Baptiste Pomet
Affiliation:
INRIA Sophia Antipolis, B.P. 93, 06902 Sophia Antipolis cedex, France; [email protected]; [email protected]
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Abstract

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

Keywords

Dynamic feedback linearizationflat control systemsMonge problemMonge equations
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 13 , Issue 2 , April 2007 , pp. 237 - 264
Copyright
© EDP Sciences, SMAI, 2007

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