Refinement of optimal control problem for practical implementation of its solution

The solution of the optimal control problem in the classical formulation is control in the form of a function of time. The implementation of such a solution leads to an open-loop control system and, therefore, cannot be applied directly in practice. It is believed that solving the classical optimal control problem leads to an optimal control program and a program trajectory in state space. To implement the motion of the control object along the program trajectory, it is necessary to build an additional motion stabilization system. The problem of synthesizing a system for stabilizing motion along a program trajectory and the requirements that this system should meet do not arise from the classical setting of the optimal control problem. A refined statement of the optimal control problem is given that includes an additional requirement for an optimal trajectory and the solution of which can be directly applied in practice in a real control object.