Adaptive synchronization design for uncertain chaotic systems in the presence of unknown system parameters: a revisit

Recently the synchronization control for chaotic systems with unknown parameters has attracted great attention among the researchers and diverse synchronization schemes have been reported in the literature. In this review article, we carefully revisit several recent articles published from 2010 to the present and find that several reported schemes are problematic. The imperfect synchronization schemes are categorized into five cases according to their defect types. By providing a general theorem for the adaptive synchronization design, we further present modified schemes to correct the defects in these articles. In addition, we have emphasized the significant linear independence condition for ensuring successful identification, as this condition has been neglected in several previous articles. We also summarize three cases when this condition is not valid, and accordingly four approaches are proposed to guarantee the successful parameter estimation for uncertain chaotic systems.

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