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Research Papers

Synchronization of Unknown Uncertain Chaotic Systems Via Adaptive Control Method

[+] Author and Article Information
Mohammad Pourmahmood Aghababa

Electrical Engineering Department,
Urmia University of Technology,
P.O. Box 57155-419,
Band Road,
Urmia, Iran
e-mail: m.p.aghababa@ee.uut.ac.ir; m.pour13@gmail.com

Bijan Hashtarkhani

Control Engineering Department,
University of Tabriz,
P.O. Box 51666-15813,
29 Bahman Blvd.,
Tabriz,Iran

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received February 20, 2014; final manuscript received July 3, 2014; published online April 2, 2015. Assoc. Editor: Stefano Lenci.

J. Comput. Nonlinear Dynam 10(5), 051004 (Sep 01, 2015) (7 pages) Paper No: CND-14-1050; doi: 10.1115/1.4027976 History: Received February 20, 2014; Revised July 03, 2014; Online April 02, 2015

In this paper, an adaptive control scheme is offered to synchronize two different uncertain chaotic systems. It is assumed that the whole dynamics of both master and slave chaotic systems and their bounds are unknown and different. The error system stabilization is achieved in two cases: with input nonlinearities and without input nonlinearities. We design an adaptive control scheme based on the state boundedness property of the chaotic systems. The proposed method does not need any information about nonlinear/linear terms of the chaotic systems. It only uses an adaptive feedback control strategy. The stability of the proposed controllers is proved by using the Lyapunov stability theory. Finally, the designed adaptive controllers are applied to synchronize two different pairs of the chaotic systems (Lorenz–Chen and electromechanical device–electrostatic transducer).

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References

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Figures

Grahic Jump Location
Fig. 1

A typical dead-zone nonlinearity function

Grahic Jump Location
Fig. 2

Synchronization errors of the Lorenz and Chen systems with linear control inputs

Grahic Jump Location
Fig. 3

Synchronization errors of the electromechanical device and electrostatic transducer with linear control inputs

Grahic Jump Location
Fig. 4

Synchronization errors of the Lorenz and Chen systems with input nonlinearities

Grahic Jump Location
Fig. 5

Synchronization errors of the electromechanical and electrostatic devices with dead-zone

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