View source for Differential Flatness of Two One-Forms in Arbitrary Number of Variables

{{HTDB paper
| authors = Muruhan Rathinam and Richard M. Murray
| title = Differential Flatness of Two One-Forms in Arbitrary Number of Variables
| source = <i>Systems and Control Letters</i>, 36:317-326, 1999.
| year = 1996
| type = Conference paper
| funding = NSF
| url = http://www.cds.caltech.edu/~murray/preprints/rm97-ecc.pdf
| 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 $(t,x^1,\dots,x^N)$. 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. If the first part
has no solution then the system is not zero-flat. 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. 
| flags = 
| tag = rm97-ecc
| id = 1996n
}}