On the Linearization of Flat Two-Input Systems by Prolongations and Applications to Control Design

TL;DR

This paper proves that all two-input flat nonlinear control systems can be made linear through prolongations, simplifying control design by avoiding the need for generalized state measurements.

Contribution

It demonstrates that any two-input flat nonlinear system can be rendered static feedback linearizable via control prolongations, impacting flatness-based control strategies.

Findings

All two-input flat systems can be linearized by prolongations.

Flatness-based tracking control can be designed with only state measurements.

The approach simplifies control implementation by avoiding generalized states.

Abstract

In this paper we consider $(x,u)$-flat nonlinear control systems with two inputs, and show that every such system can be rendered static feedback linearizable by prolongations of a suitably chosen control. This result is not only of theoretical interest, but has also important implications on the design of flatness based tracking controls. We show that a tracking control based on quasi-static state feedback can always be designed in such a way that only measurements of a (classical) state of the system, and not measurements of a generalized Brunovsky state, as reported in the literature, are required.