The control object mathematical identification problem is considered. It’s supposed, that a mathematical model is an ordinary differential equations system in Cauchi form. Therefore, the problem consists of finding right parts of differential equations system. Machine learning by symbolic regression is used for solving this problem. An example of quad-rotor spatial motion mathematical model identification is presented. Synthetic data obtained from known mathematical model are used for identification of model in the example. To obtain the training data some optimal control programs are set, and then a right parts of differential equation system a found by symbolic regression. To check a quality of identification a new optimal control problem was solved for found mathematical model. After that the found optimal solution in the form of optimal control program is used for control of the known control object model. Results of simulation are compared with a solution of the same optimal control problem for the known mathematical model.