Publication

On driftless systems with m controls and 2m or 2m-1 states that are flat by pure prolongation

Journal Article (2025)

Authors

Abstract

It is widely recognized that no tractable necessary and sufficient conditions exist for
determining whether a system is, in general, differentially flat. However, specific cases
do provide such conditions. For instance, driftless systems with two inputs have known
necessary and sufficient conditions. For driftless systems with three or more inputs, the
available conditions are only sufficient.
This paper presents new findings on determining whether a system with m inputs
and 2m or 2m − 1 states is flat by pure prolongation, a specific subclass of differen-
tial flatness. While this condition is more restrictive than general differential flatness,
the algorithm for computing flat outputs remains remarkably simple, and the verifica-
tion requirements are relatively lenient. Moreover, the conditions proposed in this work
broaden the class of systems recognized as differentially flat, as our sufficient condition
differs from existing criteria.

Categories

control theory.

Author keywords

Nonlinear control system; differential geometric control; Lie bracket; driftless system; differential flatness; pure prolongation.

Scientific reference

J. Franch and J. Lévine. On driftless systems with m controls and 2m or 2m-1 states that are flat by pure prolongation. Geometric Mechanics, 2025.