| Summary: | Background. The paper contains a refined statement of the optimal control problem, the solution of
which, in contrast to the classical formulation, can be implemented directly in a real object. For this purpose, the optimal
control problem includes the problem of synthesis of the stabilisation system of the object motion along the optimal
trajectory, which is obtained as a result of solving the classical optimal control problem. Materials and methods. To
solve the problem of stabilisation system synthesis the method of symbolic regression, method of network operator, was
applied. The real control object contains a reference model of the control object for generating the program trajectory.
An example of the solution of the refined optimal control problem of the spatial motion of a quadrocopter with phase
constraints is presented. In the first step, the optimal control problem was solved in the classical formulation and the
control function was found in the form of a piecewise linear approximation as a time function. The problem was solved
using a direct approach in which the accuracy of reaching the final state and the penalties for violating the phase
constraints were included in a single function together with a given quality criterion. An evolutionary algorithm was
used for the solution, which found sixty-eight parameters. To confirm the poor feasibility of the solution found, a
simulation of the solution obtained with a small perturbation of the initial conditions was carried out. As a result, the
solution did not reach the final state and the phase constraints were significantly violated. In the second stage, a refined
optimal control problem was solved, in which the synthesis problem of motion stabilisation along this trajectory was
solved for the obtained program trajectory. When solving the synthesis problem, the initial state was changed to a set of
initial states, and the target function was the sum of values of a given criterion for all initial states. To verify the feasibility
of the obtained solution, a simulation of the control system with perturbed initial values was carried out. Results
and conclusions. The simulation results showed that all perturbed trajectories reached the final state practically without
violating the phase constraints. In this paper, it is assumed that the obtained stabilisation system works for trajectories
of a certain class. To confirm this assumption, another optimal control problem was solved with the same phase
constraints but with a different trajectory of their circumvention. The same stabilisation system was used for the obtained
optimal control. Modelling of the perturbed solution confirmed the assumption.
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