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A novel adaptive-critic-based NN controller using reinforcement learning is developed for a class of nonlinear systems with non-symmetric dead-zone inputs. The adaptive critic NN controller uses two NNs: the critic NN is used to approximate the strategic utility function, and the output of action NN is used to approximate the unknown nonlinear function and to minimize the strategic utility function. The tuning of the NNs is performed online without an explicit offline learning phase. The uniformly ultimate boundedness of the close-loop tracking error is derived by using using the Lyapunov method. Finally, a numerical example is included to show the effectiveness of the theoretical results.