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

Issue		ESAIM: COCV Volume 13, Number 2, April-June 2007


Page(s)		237 - 264
DOI		10.1051/cocv:2007011
Published online		12 May 2007

ESAIM: COCV, Vol. 13, N°2, pp. 237-264
DOI: 10.1051/cocv:2007011

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

David Avanessoff and Jean-Baptiste Pomet

INRIA Sophia Antipolis, B.P. 93, 06902 Sophia Antipolis cedex, France; David.Avanessoff@sophia.inria.fr; Jean-Baptiste.Pomet@sophia.inria.fr

(Received April 21, 2005. Revised November 30, 2005. Published online 12 May 2007.)

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.

Mathematics Subject Classification. 93B18, 93B29, 34C20

Key words: Dynamic feedback linearization, flat control systems, Monge problem, Monge equations

© EDP Sciences, SMAI 2007

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