IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v27y2006i5p1369-1375.html
   My bibliography  Save this article

Synchronization of Genesio chaotic system via backstepping approach

Author

Listed:
  • Park, Ju H.

Abstract

Backstepping design is proposed for synchronization of Genesio chaotic system. Firstly, the control problem for the chaos synchronization of nominal Genesio systems without unknown parameters is considered. Next, an adaptive backstepping control law is derived to make the error signals between drive Genesio system and response Genesio system with an uncertain parameter asymptotically synchronized. Finally, the approach is extended to the synchronization problem for the system with three unknown parameters. The stability analysis in this article is proved by using a well-known Lyapunov stability theorem. Note that the approach provided here needs only a single controller to realize the synchronization. Two numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme.

Suggested Citation

  • Park, Ju H., 2006. "Synchronization of Genesio chaotic system via backstepping approach," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1369-1375.
    • Handle: RePEc:eee:chsofr:v:27:y:2006:i:5:p:1369-1375
    DOI: 10.1016/j.chaos.2005.05.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077905004789
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2005.05.001?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Park, Ju H., 2005. "Stability criterion for synchronization of linearly coupled unified chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1319-1325.
    2. Kim, Jae-Hun & Park, Chang-Woo & Kim, Euntai & Park, Mignon, 2005. "Adaptive synchronization of T–S fuzzy chaotic systems with unknown parameters," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1353-1361.
    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. Sharma, B.B. & Kar, I.N., 2009. "Parametric convergence and control of chaotic system using adaptive feedback linearization," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1475-1483.
    2. Hamede Karami & Saleh Mobayen & Marzieh Lashkari & Farhad Bayat & Arthur Chang, 2021. "LMI-Observer-Based Stabilizer for Chaotic Systems in the Existence of a Nonlinear Function and Perturbation," Mathematics, MDPI, vol. 9(10), pages 1-15, May.
    3. Park, Ju H., 2007. "Adaptive modified projective synchronization of a unified chaotic system with an uncertain parameter," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1552-1559.
    4. Salarieh, Hassan & Alasty, Aria, 2008. "Adaptive chaos synchronization in Chua's systems with noisy parameters," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 233-241.
    5. Handa, Himesh & Sharma, B.B., 2016. "Novel adaptive feedback synchronization scheme for a class of chaotic systems with and without parametric uncertainty," Chaos, Solitons & Fractals, Elsevier, vol. 86(C), pages 50-63.
    6. Peng, Chao-Chung & Chen, Chieh-Li, 2008. "Robust chaotic control of Lorenz system by backstepping design," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 598-608.
    7. Sahoo, Shilalipi & Nathasarma, Rahash & Roy, Binoy Krishna, 2024. "Time-synchronized predefined-time synchronization between two non-identical chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    8. Behzad, Mehdi & Salarieh, Hassan & Alasty, Aria, 2008. "Chaos synchronization in noisy environment using nonlinear filtering and sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1295-1304.
    9. Yau, Her-Terng & Chen, Chieh-Li, 2006. "Chattering-free fuzzy sliding-mode control strategy for uncertain chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 709-718.
    10. Yadav, Vijay K. & Shukla, Vijay K. & Das, Subir, 2019. "Difference synchronization among three chaotic systems with exponential term and its chaos control," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 36-51.
    11. Xuan Huang & Lingfeng Liu & Xiangjun Li & Minrong Yu & Zijie Wu, 2019. "A New Pseudorandom Bit Generator Based on Mixing Three-Dimensional Chen Chaotic System with a Chaotic Tactics," Complexity, Hindawi, vol. 2019, pages 1-9, June.
    12. Salarieh, Hassan & Shahrokhi, Mohammad, 2008. "Adaptive synchronization of two different chaotic systems with time varying unknown parameters," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 125-136.
    13. Zhang, Chaolong & Deng, Feiqi & Peng, Yunjian & Zhang, Bo, 2015. "Adaptive synchronization of Cohen–Grossberg neural network with mixed time-varying delays and stochastic perturbation," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 792-801.
    14. Lin, Chih-Min & Peng, Ya-Fu & Lin, Ming-Hung, 2009. "CMAC-based adaptive backstepping synchronization of uncertain chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 981-988.
    15. Gao, Shigen & Wang, Yubing & Dong, Hairong & Ning, Bin & Wang, Hongwei, 2017. "Controlling uncertain Genesio–Tesi chaotic system using adaptive dynamic surface and nonlinear feedback," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 180-188.
    16. Yau, Her-Terng, 2007. "Nonlinear rule-based controller for chaos synchronization of two gyros with linear-plus-cubic damping," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1357-1365.
    17. Liu, Bin & Zhou, Yiming & Jiang, Min & Zhang, Zengke, 2009. "Synchronizing chaotic systems using control based on tridiagonal structure," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2274-2281.

    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. Park, Ju H., 2007. "Adaptive modified projective synchronization of a unified chaotic system with an uncertain parameter," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1552-1559.
    2. Yu, Yongguang, 2008. "Adaptive synchronization of a unified chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 329-333.
    3. Chang, Wei-Der, 2007. "Parameter identification of Chen and Lü systems: A differential evolution approach," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1469-1476.
    4. Park, Ju H., 2005. "Chaos synchronization of a chaotic system via nonlinear control," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 579-584.
    5. Coelho, Leandro dos Santos & Bernert, Diego Luis de Andrade, 2009. "PID control design for chaotic synchronization using a tribes optimization approach," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 634-640.
    6. Park, Ju H., 2006. "Synchronization of a class of chaotic dynamic systems with controller gain variations," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1279-1284.
    7. Wang, Jiang & Si, Wenjie & Li, Huiyan, 2009. "Robust ISS-satisficing variable universe indirect fuzzy control for chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 28-38.
    8. Min, Fuhong & Luo, Albert C.J., 2012. "Periodic and chaotic synchronizations of two distinct dynamical systems under sinusoidal constraints," Chaos, Solitons & Fractals, Elsevier, vol. 45(7), pages 998-1011.
    9. Tsai, Shun-Hung & Li, Tzuu-Hseng S., 2009. "Robust fuzzy control of a class of fuzzy bilinear systems with time-delay," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2028-2040.
    10. Chen, Heng-Hui, 2009. "Chaos control and global synchronization of Liu chaotic systems using linear balanced feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 466-473.
    11. Chang, Wei-Der, 2006. "Parameter identification of Rossler’s chaotic system by an evolutionary algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1047-1053.
    12. Yu, Yongguang & Li, Han-Xiong & Duan, Jian, 2009. "Chaos synchronization of a unified chaotic system via partial linearization," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 457-463.
    13. Tarai (Poria), Anindita & Poria, Swarup & Chatterjee, Prasanta, 2009. "Synchronization of generalised linearly bidirectionally coupled unified chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 885-892.
    14. Park, Ju H., 2005. "GCS of a class of chaotic dynamic systems," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1429-1435.
    15. Wu, Xiaofeng & Cai, Jianping & Wang, Muhong, 2008. "Global chaos synchronization of the parametrically excited Duffing oscillators by linear state error feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 121-128.
    16. Vincent, U.E. & Kareem, S.O. & Nana Nbendjo, B.R. & Njah, A.N., 2015. "Quasi-synchronization dynamics of coupled and driven plasma oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 70(C), pages 85-94.
    17. Park, Ju H., 2005. "Adaptive synchronization of Rossler system with uncertain parameters," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 333-338.
    18. Feng, Yuhu & Hu, Liangjian, 2006. "On the quasi-controllability of continuous-time dynamic fuzzy control systems," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 177-188.
    19. Chen, Chung-Cheng & Hsu, Chao-Hsing & Chen, Ying-Jen & Lin, Yen-Feng, 2007. "Disturbance attenuation of nonlinear control systems using an observer-based fuzzy feedback linearization control," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 885-900.
    20. Tutueva, Aleksandra & Moysis, Lazaros & Rybin, Vyacheslav & Zubarev, Alexander & Volos, Christos & Butusov, Denis, 2022. "Adaptive symmetry control in secure communication systems," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).

    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:eee:chsofr:v:27:y:2006:i:5:p:1369-1375. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.