This paper studies the robust adaptive full state hybrid projective synchronization (FSHPS) scheme for a class of chaotic complex systems with uncertain parameters and external disturbances. By introducing a compensator and using nonlinear control and adaptive control, the robust adaptive FSHPS scheme is derived, which can eliminate the influence of uncertainties effectively and achieve adaptive FSHPS of the chaotic (hyperchaotic) complex systems asymptotically with a small error bound. The adaptive laws of the unknown parameters are given, and the sufficient conditions of realizing FSHPS are derived as well. Moreover, we also discuss the case that parameters of chaotic complex system are complex. Finally, the complex Chen system and Lü system, and the hyperchaotic complex Lorenz system are taken as two examples and the numerical simulations are provided to verify the effectiveness and robustness of the proposed control scheme.
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The authors gratefully acknowledge the suggestions of reviewers. The work was supported by the NNSF of China (Nos. 60874009 and 10971120) and the NSF of Shandong Province (No. ZR2010FM010).
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Liu, P., Liu, S. Robust adaptive full state hybrid synchronization of chaotic complex systems with unknown parameters and external disturbances. Nonlinear Dyn 70, 585–599 (2012). https://doi.org/10.1007/s11071-012-0479-y