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TECHNICAL BRIEFS

Transformations of Nonlinear Systems to High-Order Generalized Chained Forms

[+] Author and Article Information
Maria-Christina Laiou1

 Lehrstuhl für Prozesstechnik, RWTH Aachen, Templergraben 55, D-52056 Aachen, Germanylaiou@lpt.rwth-aachen.de

Alessandro Astolfi

Department of Electrical and Electronic Engineering,  Imperial College, Exhibition Road, London SW7 2BT, UKa.astolfi@imperial.ac.uk

For simplicity we use the following notation dnydtn=y(n).

It is obvious that the vector field g1 plays a special role. This is by no means necessary, e.g., it would be possible to define F=f+g2 and exchange the role of g1 and g2 in the rest of the algorithm.

1

Currently with: BMW Group, Driver Assistance Systems, Munich, Germany. E-mail: Maria-Christina.Laiou@bmw.de

J. Dyn. Sys., Meas., Control 127(4), 729-733 (Jul 30, 2004) (5 pages) doi:10.1115/1.1898234 History: Received September 23, 2003; Revised July 30, 2004

A variety of stabilization methods for nonlinear systems in chained form can be found in the literature. However, very few results exist in the area of systematically converting a general nonlinear system with two inputs to a chained form. This paper presents an algorithm for the conversion of a class of nonlinear systems with two inputs to a high-order chained, or generalized chained, form. The feedback transformation accomplishing this conversion is derived, provided certain conditions hold, by solving a system of partial differential equations. The proposed algorithm is illustrated by means of a physically motivated example, namely an under-actuated surface vessel.

Copyright © 2005 by American Society of Mechanical Engineers
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