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A robust adaptive neural network controller is proposed for a class of uncertain non-linear time-delay systems in strict feedback form with both completely unknown control gains and unknown non-symmetric dead-zone non-linearity based on backstepping design. The proposed design approach does not require a priori knowledge of the signs of the unknown control gains. The unknown time delays are compensated for constructing appropriate Lyapunov-Krasovskii functionals. By utilising integral Lyapunov design and sliding-mode control strategy, the controller singularity problem and the effect of dead-zone input non-linearity are avoided perfectly. From Lyapunov stability theorem, it is proved that the proposed design approach is able to guarantee semi-globally uniformly ultimately boundedness of all the signals in the closed-loop system, and the tracking error of the system is proven to be converged to a small neighbourhood of the origin. The simulation results demonstrate the effectiveness of the proposed approach.