Work

A dual geometric test for forward-flatness

Year: 2025

Type: article

Abstract: Forward-flatness is a generalization of static feedback linearizability and a special case of a more general flatness concept for discrete-time systems. Recently, it has been shown that this practically quite relevant property can be checked by computing a unique sequence of involutive distributions which generalizes the well-known static feedback linearization test. In this paper, a dual test for forward-flatness based on a unique sequence of integrable codistributions is derived. Since the main mathematical operations for determining this sequence are the intersection of codistributions and the calculation of Lie derivatives of 1-forms, it is computationally quite efficient. Furthermore, the formulation with codistributions also facilitates a comparison with the existing discrete-time literature regarding the closely related topic of dynamic feedback linearization, which is mostly formulated in terms of 1-forms rather than vector fields. The presented results are illustrated by two examples.

Source: Automatica

DOI: 10.1016/j.automatica.2025.112425

Authors: Bernd Kolar, Johannes Schrotshamer, Markus Schöberl

Institution: Johannes Kepler University of Linz

Language: English

Topic: Control and Stability of Dynamical Systems

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,760

Funder: Austrian Science Fund