A methodology for dynamic neural network (DNN) identification-based control of nonlinear systems is proposed. The multi-layer DNN structure is modified by the addition of a sliding mode term in order to robustly account for exogenous disturbances and DNN reconstruction errors. New weight update laws for the DNN are proposed which guarantee asymptotic regulation of the identification error to zero. The DNN identifier is used in conjunction with a continuous RISE feedback term for asymptotic tracking of a desired trajectory. Both the identifier and the controller operate simultaneously in real time.