On Necessary and Sufficient Conditions for Differential Flatness

Mathematics – Optimization and Control

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

Version 3 is the published version

Scientific paper

10.1007/s00200-010-0137-x

This paper is devoted to the characterization of differentially flat nonlinear systems in implicit representation, after elimination of the input variables, in the differential geometric framework of manifolds of jets of infinite order. We extend the notion of Lie-B\"acklund equivalence, introduced in Fliess et al. (1999), to this implicit context and focus attention on Lie-B\"acklund isomorphisms associated to flat systems, called trivializations. They can be locally characterized in terms of polynomial matrices of the indeterminate $\ddt$, whose range is equal to the kernel of the polynomial matrix associated to the implicit variational system. Such polynomial matrices are useful to compute the ideal of differential forms generated by the differentials of all possible trivializations. We introduce the notion of a strongly closed ideal of differential forms, and prove that flatness is equivalent to the strong closedness of the latter ideal, which, in turn, is equivalent to the existence of solutions of the so-called generalized moving frame structure equations. Two sequential procedures to effectively compute flat outputs are deduced and various examples and consequences are presented.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

On Necessary and Sufficient Conditions for Differential Flatness does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On Necessary and Sufficient Conditions for Differential Flatness, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Necessary and Sufficient Conditions for Differential Flatness will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-621736

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.