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Synchronization of uncertain chaotic systems via complete-adaptive-impulsive controls

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  • Li, Xian-Feng
  • Chu, Yan-Dong
  • Leung, Andrew Y.T.
  • Zhang, Hui

Abstract

The paper presents a novel synchronization scheme for uncertain chaotic systems via complete-adaptive-impulsive controls. The controllers are designed in the form of linear-error feedback coupling, but the control gains are completely adaptive. More details on minimizing interaction terms and accelerating synchronization process are revealed. The interaction terms can be selected on the largest invariant set minimally, but would be optimized corroboratively to promote the stabilization. The analytic expressions of parameter update laws for identifying uncertain parameters are derived from a reasonable truncation directly. A representative chaotic system is employed to show that the present scheme is not only a tactful way of synchronizing chaotic systems with uncertainties imposed on nonlinear terms, but a more radical approach on achieving synchronization with relatively moderate control gains than existed methods.

Suggested Citation

  • Li, Xian-Feng & Chu, Yan-Dong & Leung, Andrew Y.T. & Zhang, Hui, 2017. "Synchronization of uncertain chaotic systems via complete-adaptive-impulsive controls," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 24-30.
    • Handle: RePEc:eee:chsofr:v:100:y:2017:i:c:p:24-30
    DOI: 10.1016/j.chaos.2017.04.033
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    Cited by:

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    5. Yu, Nanxiang & Zhu, Wei, 2021. "Event-triggered impulsive chaotic synchronization of fractional-order differential systems," Applied Mathematics and Computation, Elsevier, vol. 388(C).
    6. Jiling Ding, 2017. "The Hierarchical Iterative Identification Algorithm for Multi-Input-Output-Error Systems with Autoregressive Noise," Complexity, Hindawi, vol. 2017, pages 1-11, October.
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    8. Weiqiu Pan & Tianzeng Li & Muhammad Sajid & Safdar Ali & Lingping Pu, 2022. "Parameter Identification and the Finite-Time Combination–Combination Synchronization of Fractional-Order Chaotic Systems with Different Structures under Multiple Stochastic Disturbances," Mathematics, MDPI, vol. 10(5), pages 1-26, February.
    9. Zhang, Huamin, 2018. "The eigenvalues range of a class of matrices and some applications in Cauchy–Schwarz inequality and iterative methods," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 37-48.

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