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Robust synchronization of two different fractional-order chaotic systems with unknown parameters using adaptive sliding mode approach

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Abstract

In this paper, an adaptive sliding mode control method is introduced to ensure robust synchronization of two different fractional-order chaotic systems with fully unknown parameters and external disturbances. For this purpose, a fractional integral sliding surface is defined and an adaptive sliding mode controller is designed. In this method, no knowledge of the bounds of parameters and perturbation is required in advance and the parameters are updated through an adaptive control process. The proposed scheme is global and theoretically rigorous. Two examples are given to illustrate effectiveness of the scheme, in which the synchronizations between fractional-order chaotic Chen system and fractional-order chaotic Rössler system, between fractional-order hyperchaotic Lorenz system and fractional-order hyperchaotic Chen system, respectively, are successfully achieved. Corresponding numerical simulations are also given to verify the analytical results.

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Acknowledgement

The present work is supported by Natural Science Foundation of Hebei Province under Grant No. 2010000343.

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Authors and Affiliations

  1. College of Elementary Education, Xingtai University, Xingtai, 054001, P.R. China

    Ruoxun Zhang

  2. College of Physics Science and Information Engineering, Hebei Normal University, Shijiazhuang, 050024, P.R. China

    Ruoxun Zhang & Shiping Yang

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  1. Ruoxun Zhang
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  2. Shiping Yang
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Correspondence to Shiping Yang.

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Zhang, R., Yang, S. Robust synchronization of two different fractional-order chaotic systems with unknown parameters using adaptive sliding mode approach. Nonlinear Dyn 71, 269–278 (2013). https://doi.org/10.1007/s11071-012-0659-9

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  • DOI: https://doi.org/10.1007/s11071-012-0659-9

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