Differential flatness of two one-forms in arbitrary number of variables

Abstract

Given a differentially flat system of ODEs, flat outputs that depend only on original variables but not on their derivatives are called zero-flat outputs and systems possessing such outputs are called zero-flat. In this paper we present a theory of zero-flatness for a system of two one-forms in arbitrary number of variables ( t, x 1,…, x N ). Our approach splits the task of finding zero-flat outputs into two parts. First part involves solving for distributions that satisfy a set of algebraic conditions. The second part involves finding an integrable distribution from the solution set of the first part. Typically this part involves solving PDEs. Our results are also applicable in determining if a control affine system in n states and n−2 controls has flat outputs that depend only on states. We illustrate our method by examples.