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

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  • 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.

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Yassen, M.T., 2006. "Chaos control of chaotic dynamical systems using backstepping design," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 537-548.
    6. 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.
    7. 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.
    8. 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.
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    Cited by:

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