Duality of Geometric Tests for Forward-Flatness
Optimization and Control
2025-12-23 v1 Differential Geometry
Dynamical Systems
Abstract
Recently it has been shown that the property of forward-flatness for discrete-time systems, which is a generalization of static feedback linearizability and a special case of a more general concept of flatness, can be checked by two different geometric tests. One is based on unique sequences of involutive distributions, while the other is based on a unique sequence of integrable codistributions. In this paper, the relation between these sequences is discussed and it is shown that the tests are in fact dual. The presented results are illustrated by an academic example.
Cite
@article{arxiv.2408.11143,
title = {Duality of Geometric Tests for Forward-Flatness},
author = {Johannes Schrotshamer and Bernd Kolar and Markus Schöberl},
journal= {arXiv preprint arXiv:2408.11143},
year = {2025}
}