Anti-synchronization of fractional-order chaotic complex systems with unknown parameters via adaptive control

Volume 10, Issue 11, pp 5608--5621 http://dx.doi.org/10.22436/jnsa.010.11.02

Publication Date: November 10, 2017 Submission Date: June 09, 2017

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Authors

Cuimei Jiang - School of Science, Qilu University of Technology, Jinan, Shandong 250353, P. R. China. - College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, Shandong 266590, P. R. China. Fangfang Zhang - School of Electrical Engineering and Automation, Qilu University of Technology, Jinan, Shandong 250353, P. R. China. Haiyong Qin - School of Mathematics, Qilu Normal University, Jinan, Shandong 250013, P. R. China. Tongxing Li - LinDa Institute of Shandong Provincial Key Laboratory of Network Based Intelligent Computing, Linyi University, Linyi, Shandong 276005, P. R. China. - School of Information Science and Engineering, Linyi University, Linyi, Shandong 276005, P. R. China.

Abstract

This paper is concerned with adaptive control for anti-synchronization of a class of uncertain fractional-order chaotic complex systems described by a unified mathematical expression. By utilizing the recently established result for the Caputo fractional derivative of a quadratic function and employing the adaptive control technique, we design controllers and some fractional-order parameter update laws to anti-synchronize two fractional-order chaotic complex systems with unknown parameters. The proposed method has generality, simplicity, and feasibility. Moreover, anti-synchronization between uncertain fractional-order complex Lorenz system and fractional-order complex Lu system is implemented as an example to demonstrate the effectiveness and feasibility of the proposed scheme.

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Keywords

• Adaptive control
• anti-synchronization
• fractional-order chaotic complex system
• quadratic Lyapunov function

MSC

•  34C28
•  34D06

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