The structure of dynamic neural networks and their on-line learning algorithm are two important factors for NAICSs (nonlinear adaptive inverse control system). Recurrent neural networks are effective identifiers for nonlinear plant. However, they have complex architecture. In order to simplify the structure of dynamic neural networks, this paper proposed an improved DAFNN (dynamic activation function neural network) by changing the neurons' structure. The modified DFANN with the same simple feedforward architecture as the origin one had better dynamic ability. Gradient. vectors calculation becomes the chief bottleneck for learning algorithms of DAFNNs due to its complex chain rule expansions. A new on-line learning algorithm was proposed to simplify the proceeding of gradient calculation for DAFNNs in this paper according to signal flow graph theory. The new algorithm had adaptive learning rates to guarantee its convergence. The algorithm was used as the learning algorithms of identifier and controller in NAICSs. Simulation results show it is an efficient algorithm for NAICSs.