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Research Papers

Adaptive Modified Hybrid Robust Projective Synchronization Between Identical and Nonidentical Fractional-Order Complex Chaotic Systems With Fully Unknown Parameters

[+] Author and Article Information
Hadi Delavari

Department of Electrical Engineering,
Hamedan University of Technology,
Hamedan 65155, Iran
e-mail: delavari@hut.ac.ir

Milad Mohadeszadeh

Department of Electrical Engineering,
Hamedan University of Technology,
Hamedan 65155, Iran
e-mail: m.mohadeszadeh@stu.hut.ac.ir

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received July 20, 2015; final manuscript received March 30, 2016; published online May 13, 2016. Assoc. Editor: Hiroshi Yabuno.

J. Comput. Nonlinear Dynam 11(4), 041023 (May 13, 2016) (10 pages) Paper No: CND-15-1224; doi: 10.1115/1.4033385 History: Received July 20, 2015; Revised March 30, 2016

In this paper, a robust adaptive sliding mode controller is proposed. Under the existence of external disturbances, modified hybrid projective synchronization (MHPS) between two identical and two nonidentical fractional-order complex chaotic systems is achieved. It is shown that the response system could be synchronized with the drive system up to a nondiagonal scaling matrix. An adaptive controller and parameter update laws are investigated based on the Lyapunov stability theorem. The closed-loop stability conditions are derived based on the fractional-order Lyapunov function and Mittag-Leffler function. Finally, numerical simulations are given to verify the theoretical analysis.

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Figures

Grahic Jump Location
Fig. 1

State variables of drive and response for two identical fractional-order complex chaotic T systems

Grahic Jump Location
Fig. 2

The time response of the synchronization errors between two identical fractional-order complex chaotic T systems

Grahic Jump Location
Fig. 3

The time response of the adaptive controller parameters for two identical fractional-order complex chaotic T systems

Grahic Jump Location
Fig. 4

The time response of the adaptive controller parameters for two identical fractional-order complex chaotic T systems

Grahic Jump Location
Fig. 5

State variables of drive and response for two nonidentical fractional-order complex chaotic systems

Grahic Jump Location
Fig. 6

The time response of the synchronization errors between two nonidentical fractional-order complex chaotic systems

Grahic Jump Location
Fig. 7

The time response of the adaptive controller parameters for two nonidentical fractional-order complex chaotic systems

Grahic Jump Location
Fig. 8

The time response of the adaptive controller parameters for two nonidentical fractional-order complex chaotic systems

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