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Adaptive Synchronization for a Class of Fractional Order Time-delay Uncertain Chaotic Systems via Fuzzy Fractional Order Neural Network

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  • Control Theory and Applications
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Abstract

Uncertainty and delay are common phenomena in chaotic systems, but their existence will increase the difficulty of synchronization. For the sake of actualizing synchronization of fractional order time-delay uncertain chaotic systems, we propose an adaptive fractional order fuzzy neural network synchronization scheme based on the linear matrix inequalities. A fractional order radial basis functions neural network is applied to approximate uncertainties. According to the output of the neural network, we design a general adaptive controller for fractional order time-delay uncertain chaotic systems with different topological structure. Furthermore, we propose an adaptive fractional order fuzzy neural network by introducing fuzzy rules into the network. Then the fractional order extension of the Lyapunov direct method is utilized to demonstrate the stability of the error systems under the adaptive controller. Finally, numerical simulations are conducted to verify the effectiveness of the conclusions.

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Author information

Authors and Affiliations

  1. School of Big Data and Software Engineering, Chongqing University, Chongqing, 400030, China

    Xingpeng Zhang, Xiaohong Zhang & Dan Yang

  2. College of Mathematics and Statistics, Chongqing University, Chongqing, 400030, China

    Dong Li

Authors
  1. Xingpeng Zhang
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  2. Xiaohong Zhang
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  3. Dong Li
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Corresponding author

Correspondence to Dong Li.

Additional information

Recommended by Associate Editor Guangdeng Zong under the direction of Editor Hamid Reza Karimi. The project is supported by the Qinzhou University Nurturing Fund for Projects of National Natural Science Foundation of China (No.2014PY-GJ04), the National Natural Science Foundation of China (Grant No.11202249, 61772093, 61602071) and the Fundamental Research Funds for the Central Universities (No.106112016CDJXY100006, 106112017CDJXSYY0002).

Xingpeng Zhang received his B.S. degree in Jinan University, Shandong, China, in 2012 and his M.S. degree in applied mathematics from Chongqing University, Chongqing, China, in 2015. He is currently pursuing a Ph.D. degree in software engineering from Chongqing University, China. His current research interests include dynamics of fractional order chaotic systems and deep learning.

Xiaohong Zhang received his M.S. degree in applied mathematics from Chongqing University, Chongqing, China, where he also received his Ph.D. degree in computer software and theory, in 2006. He is currently a professor in School of Software Engineering at Chongqing University. His current research interests include data mining of software engineering, topic modeling, image semantic analysis, video analysis and deep learning.

Dong Li received his B.S. and M.S. degrees in applied mathematics from Chongqing University, Chongqing, China, in 2000 and 2003, and his Ph.D. degree in engineering Chongqing University, Chongqing, China, in 2008. He is currently an Associate Professor with Chongqing University. His current research interests include nonlinear and complex system, financial mathematics and application of dynamical system, dynamical system and its application.

Dan Yang received his B.S., M.S., and Ph.D. degrees from Chongqing University, Chongqing, China, in 1982, 1985, and 1997, respectively. He is currently a professor in School of Big Data and Software Engineering at Chongqing University. His current research interests include software engineering, topic modeling, image semantic analysis and video analysis.

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Zhang, X., Zhang, X., Li, D. et al. Adaptive Synchronization for a Class of Fractional Order Time-delay Uncertain Chaotic Systems via Fuzzy Fractional Order Neural Network. Int. J. Control Autom. Syst. 17, 1209–1220 (2019). https://doi.org/10.1007/s12555-018-0342-0

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  • DOI: https://doi.org/10.1007/s12555-018-0342-0

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