The article describes the solution to the problem of stabilizing a nonlinear system using machine learning methods. Despite the existence of classical approaches for solving the optimal control problem, the need for other approaches still remains. Nowadays, solving this class of problems using artificial intelligence has become popular Neural networks are one of the promising directions in this area. The article describes a model of multilayer perceptron. A pendulum on an elastic foundation was chosen as a dynamic system for the study. To train the neural network supervised learning (backpropagation) algorithm was used. Different variants of the training sample were proposed: with pre-learning and synchronous learning. The article shows the process of stabilization of a pendulum on an elastic foundation. The closed system was built and a method for a numerical solution was implemented.