This paper considers the problem of robust tracking controller design for a nonlinear plant in which the neural network is used in the closed-loop system to estimate the nonlinear system function. We introduce the conic sector theory to the design of the robust neural control system, with the aim of providing guaranteed boundedness for both the input-output signals and the weights of the neural network. The neural network is trained by the SPSA method instead of the standard back-propagation algorithm. The proposed neural control system guarantees the closed-loop stability of the estimation, and a good tracking performance. The performance improvement of the proposed system over existing systems can be quantified in terms of preventing weight shifts, fast convergence and robustness against system disturbance.