On Triangular Forms for x-Flat Control-Affine Systems With Two Inputs

TL;DR

This paper introduces a new triangular normal form for x-flat control-affine systems with two inputs, demonstrating its broad applicability, transformation process, and an improved algorithm for identifying flat outputs.

Contribution

The paper presents a novel triangular normal form for x-flat systems and an enhanced algorithm for flat output identification, extending existing methods.

Findings

Triangular form encompasses many established normal forms.

Any x-flat system can be transformed into this form after finite prolongations.

The refined algorithm outperforms existing methods in identifying flat outputs.

Abstract

This paper examines a broadly applicable triangular normal form for x-flat control-affine systems with two inputs. First, we show that this triangular form encompasses a wide range of established normal forms. Next, we prove that any x-flat system can be transformed into this triangular structure after a finite number of prolongations of each input. Finally, we introduce a refined algorithm for identifying candidates for x-flat outputs. Through illustrative examples, we demonstrate the usefulness of our results. In particular, we show that the refined algorithm exceeds the capabilities of existing methods for computing flat outputs based on triangular forms.