IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v40y2009i3p1475-1483.html
   My bibliography  Save this article

Parametric convergence and control of chaotic system using adaptive feedback linearization

Author

Listed:
  • Sharma, B.B.
  • Kar, I.N.

Abstract

Adaptive feedback linearization control technique for chaos suppression in a chaotic system is proposed. The dynamics of the system is altered so that the closed loop model matches with a specified linear reference model. The controller parameters are assumed to be unknown and are evolved using an adaptation law that aims to drive these parameters towards their ideal values so as to achieve perfect matching between the reference and the system model. A common external forcing signal to both chaotic Genesio system and reference system is considered and adaptation laws are derived considering Lyapunov function based stability. Simulation results show that the chaotic behavior is suppressed effectively with proposed controller. Analysis of linear and nonlinear parametric convergence is also shown through simulation, both with and without excitation using suitable forcing function.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:3:p:1475-1483
    DOI: 10.1016/j.chaos.2007.09.060
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077907007679
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2007.09.060?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. Chang, Wei-Der & Yan, Jun-Juh, 2005. "Adaptive robust PID controller design based on a sliding mode for uncertain chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 167-175.
    2. Yassen, M.T., 2005. "Controlling chaos and synchronization for new chaotic system using linear feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 913-920.
    3. Yassen, M.T., 2006. "Chaos control of chaotic dynamical systems using backstepping design," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 537-548.
    4. Jayaram, A. & Tadi, M., 2006. "Synchronization of chaotic systems based on SDRE method," Chaos, Solitons & Fractals, Elsevier, vol. 28(3), pages 707-715.
    5. Park, Ju H., 2006. "Synchronization of Genesio chaotic system via backstepping approach," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1369-1375.
    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. 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.
    2. Sharma, B.B. & Kar, I.N., 2011. "Stabilization and tracking controller for a class of nonlinear discrete-time systems," Chaos, Solitons & Fractals, Elsevier, vol. 44(10), pages 902-913.
    3. Anand, Pallov & Sharma, Bharat Bhushan, 2020. "Simplified synchronizability scheme for a class of nonlinear systems connected in chain configuration using contraction," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).

    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. Lee, Keum W. & Singh, Sahjendra N., 2007. "Robust control of chaos in Chua’s circuit based on internal model principle," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1095-1107.
    2. Liu, Yong & Ren, Guodong & Zhou, Ping & Hayat, Tasawar & Ma, Jun, 2019. "Synchronization in networks of initially independent dynamical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 370-380.
    3. Peng, Ya-Fu, 2009. "Robust intelligent backstepping tracking control for uncertain non-linear chaotic systems using H∞ control technique," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2081-2096.
    4. 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.
    5. Sharma, B.B. & Kar, I.N., 2011. "Stabilization and tracking controller for a class of nonlinear discrete-time systems," Chaos, Solitons & Fractals, Elsevier, vol. 44(10), pages 902-913.
    6. Yu, Yongguang, 2008. "Adaptive synchronization of a unified chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 329-333.
    7. J. Humberto Pérez-Cruz & Pedro A. Tamayo-Meza & Maricela Figueroa & Ramón Silva-Ortigoza & Mario Ponce-Silva & R. Rivera-Blas & Mario Aldape-Pérez, 2019. "Exponential Synchronization of Chaotic Xian System Using Linear Feedback Control," Complexity, Hindawi, vol. 2019, pages 1-10, July.
    8. Jiunn-Shiou Fang & Jason Sheng-Hong Tsai & Jun-Juh Yan & Chang-He Tzou & Shu-Mei Guo, 2019. "Design of Robust Trackers and Unknown Nonlinear Perturbation Estimators for a Class of Nonlinear Systems: HTRDNA Algorithm for Tracker Optimization," Mathematics, MDPI, vol. 7(12), pages 1-20, November.
    9. Sun, Mei & Tian, Lixin & Jiang, Shumin & Xu, Jun, 2007. "Feedback control and adaptive control of the energy resource chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1725-1734.
    10. Zheng, Yongai & Ji, Zhilin, 2016. "Predictive control of fractional-order chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 307-313.
    11. Zhang, Ting & Wang, Jiang & Fei, Xiangyang & Deng, Bin, 2007. "Synchronization of coupled FitzHugh–Nagumo systems via MIMO feedback linearization control," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 194-202.
    12. Mahmoud, Gamal M. & Aly, Shaban A. & Farghaly, Ahmed A., 2007. "On chaos synchronization of a complex two coupled dynamos system," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 178-187.
    13. Yassen, M.T., 2008. "Synchronization hyperchaos of hyperchaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 465-475.
    14. 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.
    15. Maganti, Ganesh B. & Singh, Sahjendra N., 2006. "Output feedback form of Chua’s circuit and modular adaptive control of chaos using single measurement," Chaos, Solitons & Fractals, Elsevier, vol. 28(3), pages 724-738.
    16. Salarieh, Hassan & Alasty, Aria, 2009. "Chaos control in uncertain dynamical systems using nonlinear delayed feedback," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 67-71.
    17. 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.
    18. Li, Lixiang & Peng, Haipeng & Yang, Yixian & Wang, Xiangdong, 2009. "On the chaotic synchronization of Lorenz systems with time-varying lags," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 783-794.
    19. Jin, Maolin & Chang, Pyung Hun, 2009. "Simple robust technique using time delay estimation for the control and synchronization of Lorenz systems," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2672-2680.
    20. 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.

    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:40:y:2009:i:3:p:1475-1483. 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.