The problem of neural network forecasting of processes with changing laws of their behavior and imperfection of time-series samples is considered on the example of analysis of urban traffic flows. The goal is to improve the accuracy of such forecasting. To achieve this goal, we analyze the applicability of self-learning recurrent neural networks with controlled elements and the spiral structure of layers. Based on the development and application of these neural networks, the new methods and the system implementing them are proposed. These methods, in contrast to known solutions, allow continuous training of neural networks and forecasting of processes. There is no need to interrupt training to perform forecasting. For forecasting, it is possible to continuously take into account the properties of the observed processes. In addition, improved controlling of associative recall of information from the memory of recurrent neural networks is provided to improve the accuracy of forecasting. The results of traffic flow forecasting are presented. The results are compared with estimates obtained using other methods. It is shown that the proposed methods have advantages in accuracy compared to the known solutions. The developed methods are recommended for use in advanced robotic and other intelligent systems.