Nonlinear Dynamics

, Volume 76, Issue 4, pp 2059–2071 | Cite as

Hyperchaos synchronization of fractional-order arbitrary dimensional dynamical systems via modified sliding mode control

  • Ling Liu
  • Wen Ding
  • Chongxin Liu
  • Huigang Ji
  • Chuqing Cao
Original Paper


This paper considers the design of adaptive sliding mode control approach for synchronization of a class of fractional-order arbitrary dimensional hyperchaotic systems with unknown bounded disturbances. This approach is based on the principle of sliding mode control and adaptive compensation term for solving the problem of synchronization of the unknown parameters in fractional-order nonlinear systems. In particular, a novel fractional-order five dimensional hyperchaotic system has been introduced as a representative example. Furthermore, global stability and asymptotic synchronization between the outputs of master and slave systems can be achieved based on the modified Lyapunov functional and fractional stability condition. Simulation results are provided in detail to illustrate the performance of the proposed approach.


Fractional order dynamical system Hyperchaotic synchronization Sliding mode control Lyapunov methodology  Predictor–corrector algorithm 



This work was supported by National Natural Science Foundation of China (Grant Nos. 51307130 and 51177117), State Key Laboratory of Electrical Insulation and Power Equipment (Grant No. EIPE 12312).


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Ling Liu
    • 1
    • 2
  • Wen Ding
    • 1
    • 2
  • Chongxin Liu
    • 1
    • 2
  • Huigang Ji
    • 3
  • Chuqing Cao
    • 4
  1. 1.State Key Laboratory of Electrical Insulation and Power EquipmentXi’anChina
  2. 2.School of Electrical EngineeringXi’an Jiaotong UniversityXi’anChina
  3. 3.Yongji Xinshisu Electric Equipment Co., Ltd.Xi’anChina
  4. 4.Department of Electrical and Computer EngineeringNational University of SingaporeSingaporeSingapore

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