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A state space embedding approach to approximate feedback linearization of single input nonlinear control systems
Author(s) -
Deutscher Joachim,
Schmid Christian
Publication year - 2006
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1069
Subject(s) - linearization , feedback linearization , nonlinear system , control theory (sociology) , mathematics , taylor series , embedding , state space , representation (politics) , state space representation , nonlinear control , inverse , pendulum , matrix (chemical analysis) , linear system , mathematical analysis , computer science , algorithm , control (management) , physics , geometry , law , materials science , composite material , statistics , quantum mechanics , artificial intelligence , politics , political science
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.