Chaos Control of Uncertain Chaotic Systems via Backstepping Approach

[+] Author and Article Information
S. Bowong1

Laboratoire de Mathématiques Appliquées, Département de Mathématiques et Informatique, Faculté des Sciences, Université de Douala, B. P. 24157 Douala (Cameroun)sbowong@uycdc.uninet.cm

F. M. Kakmeni

Department of Physics, Faculty of Sciences, The University of Buea, P. O. Box 63 (Cameroon)fmoukam@uycdc.uninet.cm


Corresponding author. Permanent address: B.P. 12639 Yaoundé, Cameroon.

J. Vib. Acoust 128(1), 21-27 (Jan 30, 2005) (7 pages) doi:10.1115/1.2110864 History: Received May 10, 2004; Revised January 30, 2005

This paper presents a robust control scheme for a class of uncertain chaotic systems. The proposed feedback controller is composed by an uncertainty estimator and a backstepping feedback, so its implementation is quite simple and can be made on the basis of the measured signal. The developed control scheme allows chaos suppression despite uncertainties in the model as well as unmeasured disturbances. The Chua and Φ6-Duffing are used to illustrate the performance of the proposed controller.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Phase portraits of the Chua’s oscillator

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Figure 2

Chaos suppression for the Chua’s oscillator performed with k1=2 and θ=10

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Figure 3

Evolution of the current value of η (—) and its estimated value η̂ (---) for k1=2 and θ=10

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Figure 4

State x1 for three different values of the control gain k1

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Figure 5

Chaos suppression for the Φ6-Duffing equation performed k1=k2=5 and θ=30

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Figure 6

System behavior without and under control actions



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