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Flatness and Monge parameterization of two-input systems, control-affine with 4 states or general with 3 states. (English) Zbl 1178.93037
Summary: 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.

MSC:
93B18 Linearizations
93B27 Geometric methods
34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
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