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This paper focuses on a single neural network tracking control for a class of nonlinear strict-feedback systems with input dead-zone and time-varying output constraint via prescribed performance method. To release the limit condition on previous performance function that the initial tracking error needs to be known, a new modified performance function is first constructed. Further, to reduce the computational burden of traditional neural back-stepping control approaches which require all the virtual controllers to be necessarily carried out in each step, the nonlinear items are transmitted to the last step such that only one neural network is required in this design. By regarding the input-coefficients of the dead-zone slopes as a system uncertainty and introducing a new concise system transformation technique, a composite adaptive neural state-feedback control approach is developed. The most prominent feature of this scheme is that it not only owes low-computational property but also releases the previous limitations on performance function and is capable of guaranteeing the output confined within the new form of prescribed bound. Moreover, the closed-loop stability is proved using Lyapunov function. Comparative simulation is induced to verify the effectiveness. [ABSTRACT FROM AUTHOR]