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Multi-switching adaptive synchronization of two fractional-order chaotic systems with different structure and different order

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  • Control Theory and Applications
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Abstract

In this work, we combine the active and adaptive control theories, and propose a novel synchronization scheme for a class of fractional-order chaotic systems with different structure and different order. Based on the new version of fractional-order Lyapunov stability theory, we design the adaptive controllers and updating laws of different switching. We use the fractional-order Lorenz chaotic system and the fractional-order Chen chaotic system as examples to analyze the multi-switching synchronization process for fractional-order chaotic systems with different structures and different orders. Finally, numerical simulations are also given to illustrate the effectiveness and validation of the proposed method, and the model uncertainties and external disturbances are added to the considered systems to verify the robustness of the proposed controllers.

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Author information

Authors and Affiliations

  1. Information Engineering College, Henan University of Science and Technology, Luoyang, 471023, China

    Shuai Song & Xiao-Na Song

  2. Department of Mathematics, Southern Illinois University, Carbondale, Illinois, USA

    Nimisha Pathak

  3. Industrial Engineering School, University of Extremadura, Badajoz, Spain

    Ines Tejado Balsera

Authors
  1. Shuai Song
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  2. Xiao-Na Song
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  3. Nimisha Pathak
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  4. Ines Tejado Balsera
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Corresponding author

Correspondence to Xiao-Na Song.

Additional information

Recommended by Associate Editor Choon Ki Ahn under the direction of Editor Myo Taeg Lim. This work is partially supported by National Natural Science Foundation of China (Nos. 61203047, U1604146), Science and Technology Research Project in Henan Province (Nos. 152102210273, 162102410024) and China Scholarship Council (No. 201408410277). The second author would especially like to thank Prof. Om P. Agrawal and Prof. R. Koc (Chair), Department of Mechanical Engineering and Energy Processes, Southern Illinois University for hosting and providing her research facilities during April 8, 2016 to April 7, 2017.

Shuai Song received the B.S. degree from Luoyang Institute of Science and Technology, China in 2014. He is currently working toward an M.S. degree in control engineering in the Information Engineering College, Henan University of Science and Technology, Luoyang, China. His research interests include fractional-order chaotic systems and the sliding mode control.

Xiao-Na Song received her Ph.D. degree in control theory and control engineering from Nanjing University of Science and Technology, China in 2011. Now, she is an associate professor in Henan University of Science and Technology, China. Her interests include fractional-order systems, fuzzy systems and robust control.

Nimisha Pathak received her Ph.D. degree in Mathematics from Southern Illinois University, USA in August 2016. Now, she is an assistant professor in The Maharaja Sayajirao University of Baroda, India. Her interests include fractional differential equations, fractional-order systems and fractional optimal control.

Inés Tejado Balsera received her B.E., M.E., and Ph.D. degrees, the last ones with honor, in Electronic Engineering from University of Extremadura, Spain, in 2003, 2006, and 2011, respectively. Now, she is an assistant professor in that university. She has been working on fractionalorder control for more than 10 years, and has authored/coauthored over 100 research publications in peer-reviewed journals, book chapters and conference proceedings in the research field of fractional-order control. Likewise, she was involved in more than 10 research projects in such a field. Her current interests include applications in mechatronics, flexible robotics and bioengineering.

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Song, S., Song, XN., Pathak, N. et al. Multi-switching adaptive synchronization of two fractional-order chaotic systems with different structure and different order. Int. J. Control Autom. Syst. 15, 1524–1535 (2017). https://doi.org/10.1007/s12555-016-0097-4

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  • DOI: https://doi.org/10.1007/s12555-016-0097-4

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