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Optimal synchronization of Rössler system with complete uncertain parameters

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  • El-Gohary, Awad

Abstract

The paper discusses the optimal control for the chaos synchronization of Rössler systems with complete uncertain parameters during finite and infinite time intervals. Based on the Liapunov–Bellman technique, optimal control laws are derived from the conditions that ensure asymptotic stability of the error dynamical system and minimizes the cost transfer of this system from arbitrary state to its equilibrium state. The derived control laws make the states of two identical Rössler systems asymptotically synchronized. Some special cases are introduced. Important numerical simulation is included to show the effectiveness of the optimal synchronization technique.

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  • El-Gohary, Awad, 2006. "Optimal synchronization of Rössler system with complete uncertain parameters," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 345-355.
    • Handle: RePEc:eee:chsofr:v:27:y:2006:i:2:p:345-355
    DOI: 10.1016/j.chaos.2005.03.043
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    References listed on IDEAS

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    1. Yassen, M.T., 2005. "Adaptive synchronization of Rossler and Lü systems with fully uncertain parameters," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1527-1536.
    2. Yan, Jianping & Li, Changpin, 2005. "On synchronization of three chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1683-1688.
    3. Park, Ju H., 2005. "Adaptive synchronization of hyperchaotic Chen system with uncertain parameters," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 959-964.
    4. Chen, Hsien-Keng, 2005. "Global chaos synchronization of new chaotic systems via nonlinear control," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1245-1251.
    5. Park, Ju H., 2005. "Adaptive synchronization of Rossler system with uncertain parameters," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 333-338.
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    Cited by:

    1. Hao Jia & Chen Guo, 2020. "The Application of Accurate Exponential Solution of a Differential Equation in Optimizing Stability Control of One Class of Chaotic System," Mathematics, MDPI, vol. 8(10), pages 1-13, October.
    2. Sun, Fengyun & Zhao, Yi & Zhou, Tianshou, 2007. "Identify fully uncertain parameters and design controllers based on synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1677-1682.
    3. Liu, Bo & Wang, Ling & Jin, Yi-Hui & Huang, De-Xian & Tang, Fang, 2007. "Control and synchronization of chaotic systems by differential evolution algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 412-419.
    4. 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.
    5. El-Gohary, Awad & Yassen, Rizk, 2009. "Chaos and optimal control of a coupled dynamo with different time horizons," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 698-710.
    6. 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.

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