IDEAS home Printed from https://ideas.repec.org/a/hin/complx/6853826.html
   My bibliography  Save this article

Adaptive Fuzzy Synchronization of Fractional-Order Chaotic (Hyperchaotic) Systems with Input Saturation and Unknown Parameters

Author

Listed:
  • Heng Liu
  • Ye Chen
  • Guanjun Li
  • Wei Xiang
  • Guangkui Xu

Abstract

We investigate the synchronization problem of fractional-order chaotic systems with input saturation and unknown external disturbance by means of adaptive fuzzy control. An adaptive controller, accompanied with fractional adaptation law, is established, fuzzy logic systems are used to approximate the unknown nonlinear functions, and the fractional Lyapunov stability theorem is used to analyze the stability. This control method can realize the synchronization of two fractional-order chaotic or hyperchaotic systems and the synchronization error tends to zero asymptotically. Finally, we show the effectiveness of the proposed method by two simulation examples.

Suggested Citation

  • Heng Liu & Ye Chen & Guanjun Li & Wei Xiang & Guangkui Xu, 2017. "Adaptive Fuzzy Synchronization of Fractional-Order Chaotic (Hyperchaotic) Systems with Input Saturation and Unknown Parameters," Complexity, Hindawi, vol. 2017, pages 1-16, November.
    • Handle: RePEc:hin:complx:6853826
    DOI: 10.1155/2017/6853826
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/8503/2017/6853826.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/8503/2017/6853826.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2017/6853826?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Li, Junmin & Yue, Hongyun, 2015. "Adaptive fuzzy tracking control for stochastic nonlinear systems with unknown time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 514-528.
    2. C. W. J. Granger & Roselyne Joyeux, 1980. "An Introduction To Long‐Memory Time Series Models And Fractional Differencing," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 15-29, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Runzi Luo & Haipeng Su, 2018. "The Robust Control and Synchronization of a Class of Fractional-Order Chaotic Systems with External Disturbances via a Single Output," Complexity, Hindawi, vol. 2018, pages 1-8, November.
    2. Rongwei Guo & Yaru Zhang & Cuimei Jiang, 2021. "Synchronization of Fractional-Order Chaotic Systems with Model Uncertainty and External Disturbance," Mathematics, MDPI, vol. 9(8), pages 1-12, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lavička, Hynek & Kracík, Jiří, 2020. "Fluctuation analysis of electric power loads in Europe: Correlation multifractality vs. Distribution function multifractality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    2. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "The Distribution of Exchange Rate Volatility," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-059, New York University, Leonard N. Stern School of Business-.
    3. Olushina O Awe & Robert Mudida & Luis A. Gil‐Alana, 2021. "Comparative analysis of economic growth in Nigeria and Kenya: A fractional integration approach," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(1), pages 1197-1205, January.
    4. Ho, Hwai-Chung, 2015. "Sample quantile analysis for long-memory stochastic volatility models," Journal of Econometrics, Elsevier, vol. 189(2), pages 360-370.
    5. Koop, Gary & Ley, Eduardo & Osiewalski, Jacek & Steel, Mark F. J., 1997. "Bayesian analysis of long memory and persistence using ARFIMA models," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 149-169.
    6. Rob Hyndman & Heather Booth & Farah Yasmeen, 2013. "Coherent Mortality Forecasting: The Product-Ratio Method With Functional Time Series Models," Demography, Springer;Population Association of America (PAA), vol. 50(1), pages 261-283, February.
    7. Geoffrey Ngene & Kenneth A. Tah & Ali F. Darrat, 2017. "Long memory or structural breaks: Some evidence for African stock markets," Review of Financial Economics, John Wiley & Sons, vol. 34(1), pages 61-73, September.
    8. Luis Gil-Alana, 2004. "Forecasting the real output using fractionally integrated techniques," Applied Economics, Taylor & Francis Journals, vol. 36(14), pages 1583-1589.
    9. Aaron D. Smallwood & Paul M. Beaumont, 2002. "An Asymptotic MLE Approach to Modelling Multiple Frequency GARMA Models," Computing in Economics and Finance 2002 285, Society for Computational Economics.
    10. Alketa Bejko & Etleva Peta & Belinda Xarba, 2015. "The Evaluation of the Drafting Process of Regional’s Development Strategies in Albania. the Research on Gjirokastra’s Region," European Journal of Interdisciplinary Studies Articles, Revistia Research and Publishing, vol. 1, ejis_v1_i.
    11. Caporale, Guglielmo Maria & Gil-Alana, Luis & Plastun, Alex, 2018. "Is market fear persistent? A long-memory analysis," Finance Research Letters, Elsevier, vol. 27(C), pages 140-147.
    12. Gallant, A. Ronald & Hsieh, David & Tauchen, George, 1997. "Estimation of stochastic volatility models with diagnostics," Journal of Econometrics, Elsevier, vol. 81(1), pages 159-192, November.
    13. Yuri Balagula, 2020. "Forecasting daily spot prices in the Russian electricity market with the ARFIMA model," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 57, pages 89-101.
    14. Härdle, Wolfgang Karl & Hautsch, Nikolaus & Pigorsch, Uta, 2008. "Measuring and modeling risk using high-frequency data," SFB 649 Discussion Papers 2008-045, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    15. Listorti, Giulia & Esposti, Roberto, . "Horizontal Price Transmission in Agricultural Markets: Fundamental Concepts and Open Empirical Issues," Bio-based and Applied Economics Journal, Italian Association of Agricultural and Applied Economics (AIEAA), vol. 1(01), pages 1-28.
    16. Bolin Lei & Zhengdi Liu & Yuping Song, 2021. "On stock volatility forecasting based on text mining and deep learning under high‐frequency data," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(8), pages 1596-1610, December.
    17. M. E. Bontempi & M. Frigeri & R. Golinelli & M. Squadrani, 2019. "Uncertainty, Perception and the Internet," Working Papers wp1134, Dipartimento Scienze Economiche, Universita' di Bologna.
    18. SangKun Bae & Mark J. Jensen, 1998. "Long-Run Neutrality in a Long-Memory Model," Macroeconomics 9809006, University Library of Munich, Germany, revised 21 Apr 1999.
    19. Quynh-Trang Nguyen & John Francis Diaz & Jo-Hui Chen & Ming-Yen Lee, 2019. "Fractional Integration in Corporate Social Responsibility Indices: A FIGARCH and HYGARCH Approach," Asian Economic and Financial Review, Asian Economic and Social Society, vol. 9(7), pages 836-850, July.
    20. Giorgio Canarella & Luis A. Gil-Alana & Rangan Gupta & Stephen M. Miller, 2020. "Modeling US historical time-series prices and inflation using alternative long-memory approaches," Empirical Economics, Springer, vol. 58(4), pages 1491-1511, April.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hin:complx:6853826. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.