On an implicit triangular decomposition of nonlinear control systems that are 1-flat - a constructive approach

TL;DR

This paper introduces a constructive method to transform nonlinear multi-input control systems into an implicit triangular form based on differential equations, generalizing the Brunovsky form for flat systems.

Contribution

It proposes a new implicit triangular decomposition for nonlinear control systems and a constructive approach to achieve this form, extending existing linearization techniques.

Findings

The method generalizes Brunovsky form for nonlinear systems.

Constructive procedure for triangular form transformation.

Identification of variables with explicit evolution without integration.

Abstract

We study the problem to provide a triangular form based on implicit differential equations for non-linear multi-input systems with respect to the flatness property. Furthermore, we suggest a constructive method for the transformation of a given system into that special triangular shape, if possible. The well known Brunovsky form, which is applicable with regard to the exact linearization problem, can be seen as special case of this implicit triangular form. A key tool in our investigation will be the construction of Cauchy characteristic vector fields that additionally annihilate certain codistributions. In adapted coordinates this construction allows to single out variables whose time-evolution can be derived without any integration.