The Advanced Optimal Control Problem and Approach to Its Numerical Solving

It is well known that the solution of the optimal control problem in the classical formulation does not allow to obtain control that is directly applied in a real object because the resulting control function is a function of time and its application to a real object leads to the creation of an open loop control system sensitive to small disturbances. In order to implement real object control, a feedback control function dependent on the state vector of the control object must be constructed. The construction of such a function does not follow in any way from the classical setting of the optimal control problem. The work provides an advanced formulation of the optimal control problem, which formally requires the construction of a control function in feedback. To solve this formulated problem and to obtain a feedback control function the numerical approach on the base applying symbolic regression for machine learning of control is proposed. As an example, the problem of optimal control of the spatial movement of the quadcopter for detailed reconnaissance of the region, for example, for the purpose of demining it, is considered.