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A Takagi-Suegeno-Kang (TSK) fuzzy cerebellar-model-articulation-controller-based robust adaptive backstepping (TFCRAB) control system is proposed for the uncertain nonlinear systems. This TFCRAB control system is composed of a novel TSK fuzzy cerebellar model articulation controller (TFC) and a robust compensator. The proposed TFC is a generalization of a TSK fuzzy system, a fuzzy neural network, and a conventional cerebellar-model-articulation-controller. It is used as the principal tracking controller to mimic an ideal backstepping controller (IBC). The parameters of TFC are tuned online by the derived adaptation laws based on the Lyapunov stability theorem. The robust compensator is designed to dispel the approximation error between the TFC and the IBC so that the asymptotic stability of the closed-loop system can be guaranteed. Finally, the proposed control system is applied to control a Duffing-Holmes chaotic system and a voice coil motor. From the simulation and experimental results, it is verified that the proposed TFCRAB control scheme can achieve favorable tracking performance and that even the system models of the controlled systems are unknown.