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Research Papers

Adaptive Sliding Mode Control for Synchronization of a Fractional-Order Chaotic System

[+] Author and Article Information
Chunlai Li

e-mail: lichunlai33@126.com

Kalin Su

College of Physics and Electronics,
Hunan Institute of Science and Technology,
Yueyang 414006,China

Lei Wu

No. 6 Department,
Air Force Paratrooper College,
Guilin 541003,China

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received June 11, 2012; final manuscript received October 7, 2012; published online November 28, 2012. Assoc. Editor: J. A. Tenreiro Machado.

J. Comput. Nonlinear Dynam 8(3), 031005 (Nov 28, 2012) (7 pages) Paper No: CND-12-1089; doi: 10.1115/1.4007910 History: Received June 11, 2012; Revised October 07, 2012

This paper proposes a three-dimensional autonomous chaotic system which displays some interest dynamical behaviors such as invariable Lyapunov exponent spectrums and controllable signal amplitude. The corresponding fractional version of the proposed system is obtained. A single state controller for synchronization of this fractional-order chaotic system is developed based on the techniques of sliding mode control and adaptive control. Numerical simulations are provided to demonstrate the feasibility of the presented synchronization method.

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Figures

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Fig. 1

(a) x1-x2 phase portrait; (b) x2- x3 phase portrait; (c) x1-x3 phase portrait

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Fig. 2

Bifurcation diagrams system, Eq. (1), versus: (a) parameter a; (b) parameter b; (c) parameter c

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Fig. 3

(a) Lyapunov exponent spectrum versus d; (b) signal amplitude curve versus d

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Fig. 4

(a) Lyapunov exponent spectrum versus e; (b) signal amplitude curve versus e

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Fig. 5

(a) Lyapunov exponent spectrum versus f; (b) signal amplitude curve versus f

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Fig. 6

Phase portrait and time series of system, Eq. (1). (a) phase portrait; (b) time series.

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Fig. 7

Chaotic attractor of fractional-order system, Eq. (9)

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Fig. 8

Synchronization result: (a) time response of the states, (b) synchronization error

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Fig. 9

Projective synchronization result: (a) time response of the states, (b) synchronization error

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