*Proceeding Paper* **Stabilization of Movement along an Optimal Trajectory and Its Solution †**

**Askhat Diveev 1,\*, Elena Sofronova 1, Nurbek Konyrbaev <sup>2</sup> and Ainur Bexeitova <sup>2</sup>**


**Abstract:** The extended optimal control problem is considered. It is necessary to find an optimal control function, that not only provides the achievement of terminal state with optimal value of the given quality criterion, but also is implemented in the control system of a real object. It means, that the control function should depend on the state space vector, and the optimal solution should keep optimality property at small perturbations of the found solution. To solve this problem machine learning control by symbolic regression is used. In the extended optimal control problem, the problem statement of stabilization system synthesis for movement along the optimal trajectory is included. Synthesis problem is solved by the network operator method. In the synthesis problem a domain of initial conditions is considered instead of one point of initial state. It provides less sensitivity of found solution to perturbations of initial states. An example of solving the extended optimal control problem with complex phase constraints in the form of bottleneck for four quadcopters is presented.

**Keywords:** optimal control; stabilization system; control synthesis; symbolic regression; evolutionary computations
