A Flat Triangular Structure Based on a Multi-Chained Form

TL;DR

This paper introduces a new flat triangular form for multi-input control-affine systems, providing geometric characterizations and constructive methods to determine differential flatness, which simplifies control design.

Contribution

It presents a novel structurally flat triangular form based on a multi-chained form for systems with three or more inputs, including complete geometric characterizations and flat output computation procedures.

Findings

Complete geometric characterizations for specific instances.

Sufficient conditions for differential flatness.

Constructive procedures for flat output computation.

Abstract

Determining whether a nonlinear multi-input system is differentially flat remains challenging. One way to obtain computationally tractable sufficient conditions is to give complete characterizations of flat normal forms. We introduce a structurally flat triangular form for control-affine systems with at least three inputs that is based on a multi-chained form. For two specific instances of this structure, we provide complete geometric characterizations, i.e., necessary and sufficient conditions under which a control-affine system is static-feedback equivalent to the respective triangular form. These characterizations yield sufficient conditions for differential flatness and, in turn, constructive procedures for computing flat outputs.