FLATNESS AND MONGE PARAMETERIZATION OF TWO-INPUT SYSTEMS, CONTROL-AFFINE WITH 4 STATES OR GENERAL WITH 3 STATES

摘要

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.