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

Avanessoff, David; Pomet, Jean-Baptiste

ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 2, pp. 237-264.

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.

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