In the absence of any observation system or low veracity of the data, it is possible to provide control over a limited time interval basing on a high-precision control object model used. The paper proposes to use a multilayer artificial neural network (ANN) to obtain such a model. In this case, instead of the ordinary differential equation (ODE) system in the Cauchy form, we get a mixed ODE-ANN mathematical model, the parameters of which are tuned to the dynamics of a particular control object. The paper describes the process of identification of the control object model including obtaining a sufficient volume of the training sample. General data properties are formulated to obtain a good model from the point of view of use in control problems. The problem of optimal control for an object described with ANN-based model is formulated and numerical approach for its solution is proposed. An example of solving the optimal control problem for a mobile robot based on the identified neural network model is given.