In the modern world, artificial neural networks are actively penetrating into those areas where the use of traditional algorithms did not allow achieving satisfactory results. Most of the responsibilities in these areas previously lay entirely on the shoulders of humans. Therefore, it is not surprising that, despite the complexity of modern control objects, neural networks can be implemented in automatic control systems to solve problems of varying degrees of complexity due to their adaptability, learning ability and accurate approximation of data that correlate with each other in a very non-obvious way. That is why they are well suited for working with control objects, the mathematical model of which is highly complex and has significant nonlinearities. For example, if it is not well known, then its behavior can be approximated by a low-order model in order to pre-set the matrices of the artificial neural network for the purpose of its further training on a real control object.