Nowadays, in the field of information processing, neural networks (NNs) are very used, because they can learn adaptively how to behave in a desired way. In the field of adaptive control, NNs are the most beneficial when the system to be controlled is not known in advance, because the system can be modeled by NNs to predict its behavior. In this case, it is very important how accurate the estimation of the NN is, since if the approximation is too rough then extra calculations are needed to get better results. One of the possibilities for improving the NN model is on-line learning during the control process, but this option requires high computational time. Another possibility is the application of Robust Fixed Point Transformations (RFPT), since though, it can only guarantee local stability, RFPT has been developed to reduce the inaccuracy caused by modeling errors and it does not need high computational time. In this paper, a new combination of the two methods the on-line trained neural networks and RFPT is proposed to decrease the computational burden caused by the on-line adaptation and keep the results close to optimum.