Approximate Feedback Linearization: A Normal Form Approach

[+] Author and Article Information
S. Talwar, N. Sri Namachchivaya, P. G. Voulgaris

Nonlinear Systems Group, Department of Aeronautical and Astronautical Engineering, University of Illinols at Urbana-Champaign, Urbana, IL 61801

J. Dyn. Sys., Meas., Control 118(2), 201-210 (Jun 01, 1996) (10 pages) doi:10.1115/1.2802305 History: Received March 04, 1994; Online December 03, 2007


The emerging field of nonlinear control theory has attempted to alleviate the problem associated with applying linear control theory to nonlinear problems. A segment of nonlinear control theory, called exact feedback linearization, has proven useful in a class of problems satisfying certain controllability and integrability constraints. Approximate feedback linearization has enlarged this class by weakening the integrability conditions, but application of both these techniques remains limited to problems in which a series of linear partial differential equations can easily be solved. By use of the idea of normal forms, from dynamical systems theory, an efficient method of obtaining the necessary coordinate transformation and nonlinear feedback rules is given. This method, which involves the solution of a set of linear algebraic equations, is valid for any dimensional system and any order nonlinearity provided it meets the approximate feedback linearization conditions.

Copyright © 1996 by The American Society of Mechanical Engineers
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