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A state space embedding approach to approximate feedback linearization of single input nonlinear control systems

✍ Scribed by Joachim Deutscher; Christian Schmid

Publisher: John Wiley and Sons
Year: 2006
Tongue: English
Weight: 274 KB
Volume: 16
Category: Article
ISSN: 1049-8923
DOI: 10.1002/rnc.1069

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✦ Synopsis

Abstract

This contribution presents a numerical approach to approximate feedback linearization which transforms the Taylor expansion of a single input nonlinear system into an approximately linear system by considering the terms of the Taylor expansion step by step. In the linearization procedure, higher degree terms are taken into account by using a state space embedding such that the corresponding system representation has not to be computed in every linearization step. Linear matrix equations are explicitly derived for determining the nonlinear change of coordinates and the nonlinear feedback that approximately linearize the nonlinear system. If these linear matrix equations are not solvable, a least square solution by applying the Moore–Penrose inverse is proposed. The results of the paper are illustrated by the approximate feedback linearization of an inverted pendulum on a cart. Copyright © 2006 John Wiley & Sons, Ltd.

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