IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v41y2009i5p2672-2680.html
   My bibliography  Save this article

Simple robust technique using time delay estimation for the control and synchronization of Lorenz systems

Author

Listed:
  • Jin, Maolin
  • Chang, Pyung Hun

Abstract

This work presents two simple and robust techniques based on time delay estimation for the respective control and synchronization of chaos systems. First, one of these techniques is applied to the control of a chaotic Lorenz system with both matched and mismatched uncertainties. The nonlinearities in the Lorenz system is cancelled by time delay estimation and desired error dynamics is inserted. Second, the other technique is applied to the synchronization of the Lü system and the Lorenz system with uncertainties. The synchronization input consists of three elements that have transparent and clear meanings.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:5:p:2672-2680
    DOI: 10.1016/j.chaos.2008.09.055
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077908004566
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2008.09.055?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. Mou, Chen & Jiang, Chang-sheng & Bin, Jiang & Wu, Qing-xian, 2009. "Sliding mode synchronization controller design with neural network for uncertain chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1856-1863.
    2. Yassen, M.T., 2006. "Chaos control of chaotic dynamical systems using backstepping design," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 537-548.
    3. Layeghi, Hamed & Arjmand, Mehdi Tabe & Salarieh, Hassan & Alasty, Aria, 2008. "Stabilizing periodic orbits of chaotic systems using fuzzy adaptive sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1125-1135.
    4. Bonakdar, Mohammad & Samadi, Mostafa & Salarieh, Hassan & Alasty, Aria, 2008. "Stabilizing periodic orbits of chaotic systems using fuzzy control of Poincaré map," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 682-693.
    5. López-Mancilla, Didier & Cruz-Hernández, César, 2008. "Output synchronization of chaotic systems under nonvanishing perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1172-1186.
    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. Chen, Wei-Ching, 2008. "Dynamics and control of a financial system with time-delayed feedbacks," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1198-1207.
    8. Yau, Her-Terng & Chen, Chieh-Li, 2007. "Chaos control of Lorenz systems using adaptive controller with input saturation," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1567-1574.
    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. Dali, Ali & Abdelmalek, Samir & Bakdi, Azzeddine & Bettayeb, Maamar, 2023. "A class of PSO-tuned controllers in Lorenz chaotic system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 430-449.

    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. Salarieh, Hassan & Alasty, Aria, 2008. "Adaptive control of chaotic systems with stochastic time varying unknown parameters," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 168-177.
    2. Poursamad, Amir & Markazi, Amir H.D., 2009. "Adaptive fuzzy sliding-mode control for multi-input multi-output chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3100-3109.
    3. Salarieh, Hassan & Alasty, Aria, 2009. "Chaos control in an economic model via minimum entropy strategy," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 839-847.
    4. Coelho, Leandro dos Santos & Araujo, Ernesto, 2009. "Identification of the Hénon chaotic map by fuzzy modeling and Nelder–Mead simplex method," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2762-2772.
    5. dos Santos Coelho, Leandro & Coelho, Antonio Augusto Rodrigues, 2009. "Model-free adaptive control optimization using a chaotic particle swarm approach," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2001-2009.
    6. Qijia Yao & Hadi Jahanshahi & Stelios Bekiros & Jinping Liu & Abdullah A. Al-Barakati, 2023. "Fixed-Time Adaptive Chaotic Control for Permanent Magnet Synchronous Motor Subject to Unknown Parameters and Perturbations," Mathematics, MDPI, vol. 11(14), pages 1-14, July.
    7. Baishya, Chandrali & Premakumari, R.N. & Samei, Mohammad Esmael & Naik, Manisha Krishna, 2023. "Chaos control of fractional order nonlinear Bloch equation by utilizing sliding mode controller," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    8. Gao, Richie, 2019. "A novel track control for Lorenz system with single state feedback," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 236-244.
    9. Dadras, Sara & Momeni, Hamid Reza & Majd, Vahid Johari, 2009. "Sliding mode control for uncertain new chaotic dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1857-1862.
    10. 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.
    11. Layeghi, Hamed & Arjmand, Mehdi Tabe & Salarieh, Hassan & Alasty, Aria, 2008. "Stabilizing periodic orbits of chaotic systems using fuzzy adaptive sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1125-1135.
    12. César Cruz-Díaz & Basilio del Muro-Cuéllar & Gonzalo Duchén-Sánchez & Juan Francisco Márquez-Rubio & Martín Velasco-Villa, 2022. "Observer-Based PID Control Strategy for the Stabilization of Delayed High Order Systems with up to Three Unstable Poles," Mathematics, MDPI, vol. 10(9), pages 1-17, April.
    13. 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.
    14. Chen, Mou & Chen, Wen-hua, 2009. "Robust adaptive neural network synchronization controller design for a class of time delay uncertain chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2716-2724.
    15. Veronika NOVOTNA & Stanislav Å KAPA & Bernard NEUWIRTH, 2019. "Analysis Of A Non-Linear Dynamic Financial System," Proceedings of the INTERNATIONAL MANAGEMENT CONFERENCE, Faculty of Management, Academy of Economic Studies, Bucharest, Romania, vol. 13(1), pages 288-297, November.
    16. Haghighatdar, F. & Ataei, M., 2009. "Adaptive set-point tracking of the Lorenz chaotic system using non-linear feedback," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1938-1945.
    17. Zheng, Yongai & Ji, Zhilin, 2016. "Predictive control of fractional-order chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 307-313.
    18. Ding, Yuting & Jiang, Weihua & Wang, Hongbin, 2012. "Hopf-pitchfork bifurcation and periodic phenomena in nonlinear financial system with delay," Chaos, Solitons & Fractals, Elsevier, vol. 45(8), pages 1048-1057.
    19. Kocamaz, Uğur Erkin & Cevher, Barış & Uyaroğlu, Yılmaz, 2017. "Control and synchronization of chaos with sliding mode control based on cubic reaching rule," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 92-98.
    20. Çalış, Yasemin & Demirci, Ali & Özemir, Cihangir, 2022. "Hopf bifurcation of a financial dynamical system with delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 343-361.

    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:41:y:2009:i:5:p:2672-2680. 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.