Nonlinear Dynamics

, Volume 71, Issue 1, pp 269–278

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

Original Paper

DOI: 10.1007/s11071-012-0659-9

Cite this article as:
Zhang, R. & Yang, S. Nonlinear Dyn (2013) 71: 269. doi:10.1007/s11071-012-0659-9


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.


Adaptive sliding mode controlChaos synchronizationFractional-order chaotic systemUnknown parameter

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.College of Elementary EducationXingtai UniversityXingtaiP.R. China
  2. 2.College of Physics Science and Information EngineeringHebei Normal UniversityShijiazhuangP.R. China