It is known that solving the classical problem of optimal control leads to obtaining a control function, as a function of time, which cannot be implemented directly in the control system of a real object, since the resulting control system is open-loop one. It is proposed to use the method of the extended model of the control object. Initially, a universal system for stabilizing the movement of an object along any trajectory in the space of states from a certain class is synthesized for the object model. This stabilization system is built into the control object. The original reference model of the control object is then added to the object with a free control vector on the right side. Thus, the extended object model includes an object model with a motion stabilization system and a reference model. The optimal control problem is solved for the extended model. In the synthesis of a universal stabilization system, machine learning by symbolic regression is used. An example of solving the problem of optimal control of a wheel robot with a differential drive is given.

A new numerical method for solving the optimal control problem in class practically implemented solutions is presented. The method uses an approach of the synthesized control and takes account uncertainties of initial states. Like as synthesized control the method move a control object changing location of stable equilibrium point. As a result it chooses from all possible optimal synthesized controls such, that less sensitive to changes of initial states. As an example, the optimal control problem of quadcopter with complex phase constraints in the form of obstacle areas and narrow bottle neck is considered. To solve this problem firstly the synthesis control problem is solved for obtaining stable equilibrium point in the state space by symbolic regression. After that positions of stable equilibrium points are searched according to source functional from the optimal control problem. As an example, the optimal control problem of quadcopter with complex phase constraints in the form of obstacle areas and narrow bottle neck is considered. To solve this problem firstly the synthesis control problem is solved for obtaining stable equilibrium point in the state space by symbolic regression. After that positions of stable equilibrium points are searched according to source functional from the optimal control problem. Additionally at the search of equilibrium point positions the goal functional is calculated as a sum of fuctional values for all given points of initial states.