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Research Papers

Adaptive Finite-Time Synchronization of Non-Autonomous Chaotic Systems With Uncertainty

[+] Author and Article Information
Mohammad Pourmahmood Aghababa

Electrical Engineering Department,
Urmia University of Technology,
Urmia, Iran
e-mail: m.p.aghababa@ee.uut.ac.ir;
m.pour13@gmail.com

Hasan Pourmahmood Aghababa

Department of Mathematics,
University of Tabriz,
Tabriz, Iran;
Research Center for Industrial Mathematics of University of Tabriz,
Tabriz, Iran
e-mail: h_p_aghababa@tabrizu.ac.ir

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 18, 2011; final manuscript received November 4, 2012; published online December 19, 2012. Assoc. Editor: Claude-Henri LAMARQUE.

J. Comput. Nonlinear Dynam 8(3), 031006 (Dec 19, 2012) (11 pages) Paper No: CND-11-1220; doi: 10.1115/1.4023007 History: Received November 18, 2011; Revised November 04, 2012

Due to its useful applications in real world processes, synchronization of chaotic systems has attracted the attention of many researchers of mathematics, physics and engineering sciences. In practical situations, many chaotic systems are inevitably disturbed by model uncertainties and external disturbances. Furthermore, in practice, it is hard to determine the precise values of the chaotic systems’ parameters in advance. Besides, from a practical point of view, it is more desirable to achieve synchronization in a given finite time. In this paper, we investigate the problem of finite-time chaos synchronization between two different chaotic systems in the presence of model uncertainties, external disturbances and unknown parameters. Both autonomous and non-autonomous chaotic systems are taken into account. To tackle the unknown parameters, appropriate adaptation laws are proposed. Using the adaptation laws and finite-time control technique, an adaptive robust finite-time controller is designed to guarantee that the state trajectories slave system converge to the state trajectories of the master system in a given finite time. Some numerical simulations are presented to verify the robustness and usefulness of the proposed finite-time control technique.

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References

Figures

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Fig. 7

Phase portraits of the chaotic electromechanical device

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Fig. 8

Synchronization errors of the electrostatic transducer and electromechanical device

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Fig. 9

State trajectories of the synchronized electrostatic transducer and electromechanical device

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Fig. 10

Time histories of the applied control inputs, Eq. (43)

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Fig. 1

Synchronization errors of the Lorenz and Chen systems

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Fig. 2

State trajectories of the synchronized Lorenz and Chen systems

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Fig. 3

Time histories of the applied control inputs, Eq. (36)

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Fig. 4

Schematic diagram of the electrostatic transducer [38]

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Fig. 5

Strange attractors of the chaotic electrostatic transducer

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Fig. 6

Schematic diagram of the electromechanical device [38]

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