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This paper presents a composite learning fuzzy control to synchronize two different uncertain incommensurate fractional-order time-varying delayed chaotic systems with unknown external disturbances and mismatched parametric uncertainties via the Takagi-Sugeno fuzzy method. An adaptive controller together with fractional-order composite learning laws is designed based on both a parallel distributed compensation technology and a fractional Lyapunov criterion. The boundedness of all variables in the closed-loop system and the Mittag-Leffler stability of tracking error can be guaranteed. T-S fuzzy systems are provided to tackle unknown nonlinear functions. The distinctive features of the proposed approach consist in the following: (1) a supervisory control law is designed to compensate the lumped disturbances; (2) both the prediction error and the tracking error are used to estimate the unknown fuzzy system parameters; (3) parameter convergence can be ensured by an interval excitation condition. Finally, the feasibility of the proposed control strategy is demonstrated throughout an illustrative example.

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