*Article* **Machine Learning Control Based on Approximation of Optimal Trajectories**

**Askhat Diveev 1, Sergey Konstantinov 2, Elizaveta Shmalko 1,\* and Ge Dong <sup>3</sup>**


**Abstract:** The paper is devoted to an emerging trend in control—a machine learning control. Despite the popularity of the idea of machine learning, there are various interpretations of this concept, and there is an urgent need for its strict mathematical formalization. An attempt to formalize the concept of machine learning is presented in this paper. The concepts of an unknown function, work area, training set are introduced, and a mathematical formulation of the machine learning problem is presented. Based on the presented formulation, the concept of machine learning control is considered. One of the problems of machine learning control is the general synthesis of control. It implies finding a control function that depends on the state of the object, which ensures the achievement of the control goal with the optimal value of the quality criterion from any initial state of some admissible region. Supervised and unsupervised approaches to solving a problem based on symbolic regression methods are considered. As a computational example, a problem of general synthesis of optimal control for a spacecraft landing on the surface of the Moon is considered as supervised machine learning control with a training set.

**Keywords:** machine learning control; general synthesis problem; symbolic regression; optimal control; evolutionary algorithm
