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Optimal control and synchronization of Lorenz system with complete unknown parameters

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  • El-Gohary, Awad
  • Sarhan, Ammar

Abstract

The paper discusses the optimal control and synchronization problems of Lorenz systems with fully unknown parameters. Based on the Liapunov–Bellman technique, the optimal control law with three-state variables feedback is derived such that the trajectory of the Lorenz system is optimally stabilized to an equilibrium point of the uncontrolled system. Further, another optimal control law is also applied to achieve the state synchronization of two identical Lorenz systems. Numerical results to demonstrate the effectiveness of the proposed control scheme.

Suggested Citation

  • El-Gohary, Awad & Sarhan, Ammar, 2006. "Optimal control and synchronization of Lorenz system with complete unknown parameters," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1122-1132.
    • Handle: RePEc:eee:chsofr:v:30:y:2006:i:5:p:1122-1132
    DOI: 10.1016/j.chaos.2005.09.025
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    References listed on IDEAS

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    1. El-Gohary, Awad, 2006. "Optimal synchronization of Rössler system with complete uncertain parameters," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 345-355.
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    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.
    2. Wu, Fuqiang & Zhou, Ping & Alsaedi, Ahmed & Hayat, Tasawar & Ma, Jun, 2018. "Synchronization dependence on initial setting of chaotic systems without equilibria," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 124-132.
    3. El-Gohary, Awad & Yassen, Rizk, 2006. "Adaptive control and synchronization of a coupled dynamo system with uncertain parameters," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1085-1094.
    4. Zelinka, Ivan & Senkerik, Roman & Navratil, Eduard, 2009. "Investigation on evolutionary optimization of chaos control," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 111-129.
    5. Peng, Ya-Fu, 2009. "Robust intelligent sliding model control using recurrent cerebellar model articulation controller for uncertain nonlinear chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 150-167.

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