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Research Papers

Robust Adaptive Synchronization of Chaotic Systems With Nonsymmetric Input Saturation Constraints

[+] Author and Article Information
Samaneh Mohammadpour

Department of Electrical and
Electronic Engineering,
Shiraz University of Technology,
Modares Boulevard,
P.O. Box 71555-313,
Shiraz 71557-13876, Iran
e-mail: s.mohamadpor@sutech.ac.ir

Tahereh Binazadeh

Department of Electrical and
Electronic Engineering,
Shiraz University of Technology,
Modares Boulevard,
P.O. Box 71555-313,
Shiraz 71557-13876, Iran
e-mail: binazadeh@sutech.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 22, 2016; final manuscript received August 8, 2017; published online October 9, 2017. Assoc. Editor: Katrin Ellermann.

J. Comput. Nonlinear Dynam 13(1), 011005 (Oct 09, 2017) (7 pages) Paper No: CND-16-1574; doi: 10.1115/1.4037672 History: Received November 22, 2016; Revised August 08, 2017

This paper considers the robust synchronization of chaotic systems in the presence of nonsymmetric input saturation constraints. The synchronization happens between two nonlinear master and slave systems in the face of model uncertainties and external disturbances. A new adaptive sliding mode controller is designed in a way that the robust synchronization occurs. In this regard, a theorem is proposed, and according to the Lyapunov approach the adaptation laws are derived, and it is proved that the synchronization error converges to zero despite of the uncertain terms in master and slave systems and nonsymmetric input saturation constraints. Finally, the proposed method is applied on chaotic gyro systems to show its applicability. Computer simulations verify the theoretical results and also show the effective performance of the proposed controller.

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Figures

Grahic Jump Location
Fig. 1

Phase trajectory of the nominal chaotic gyro system

Grahic Jump Location
Fig. 2

Time-responses of synchronization errors without applying the proposed controller

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Fig. 3

Time-responses of state variables of the master and slave systems by applying the proposed controller: (a)x1(t),y1(t) and (b)x2(t),y2(t)

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Fig. 4

Time-response of the sliding surface

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Fig. 5

Time-responses of the synchronization errors with uH=3 and−uL=−4 : (a) by saturated control signal given in Ref. [36] and (b) by the proposed saturated control signal

Grahic Jump Location
Fig. 6

Time-responses of the saturated control signal with uH=3 and−uL=−4 : (a) given controller in Ref. [38] and (b) proposed controller in this paper

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Fig. 7

Time-responses of parameters η(t),λ̂(t), and γ1(t)

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