Dynamic feedback linearization of two-input control systems via successive one-fold prolongations

TL;DR

This paper introduces a constructive algorithm for dynamically linearizing two-input control systems through successive prolongations, expanding the class of systems that can be linearized beyond static feedback methods.

Contribution

It presents a novel algorithm that uses successive one-fold prolongations and involutive subdistributions to achieve dynamic feedback linearization of control systems.

Findings

Algorithm is constructive and provides sufficient conditions for flatness.

It extends linearization techniques to systems with non-involutive distributions.

The method is a dual approach to existing dynamic feedback linearization algorithms.

Abstract

In this paper, we propose a constructive algorithm to dynamically linearize two-input control systems via successive one-fold prolongations of a control that has to be suitably chosen at each step of the algorithm. Linearization via successive one-fold prolongations requires special properties of the linearizability distributions $\mathcal{D}^0 \subset \mathcal{D}^1 \subset\mathcal{D}^2 \subset \cdots$. Contrary to the case of static feedback linearizability, they need not be involutive but the first noninvolutive one has to contain an involutive subdistribution of corank one. The main idea of the proposed algorithm is to replace, at each step, the first noninvolutive distribution by its involutive subdistribution of corank one, thus for the prolonged system we gain at least one new involutive distribution. Our algorithm is constructive, gives sufficient conditions for flatness, and can be seen as the dual of the dynamic feedback linearization algorithm of Battilotti and Califano [2003, 2005].