Extended Optimal Control Problem for Practical Application

To apply a solution of the optimal control problem directly to the control object for which model this problem was solved, it is necessary to build a system of motion stabilization along the obtained optimal trajectory. However, the construction of such a stabilization system is not provided in the classical formulation of the optimal control problem. Therefore, additional requirements for the properties of the optimal solution have been introduced into the optimal control problem. A formulation of the extended optimal control problem is introduced and the approaches to its numerical solution are discussed. One way to meet the introduced requirements is to build a stabilization motion system of an object along a program trajectory. As far as stabilization to the whole program trajectory, not from point to point on this trajectory, is rather challenging task, so for this, numerical methods of symbolic regression are proposed to be applied. The approach consists in application of machine learning by symbolic regression to the control synthesis problem. Symbolic regression allows to find a mathematical expression for control function as a function of the state space vector. Computational example of solving the extended optimal control problem for a robot group is presented. It is shown experimentally, that the solution of the extended optimal control problem is much less sensitive to disturbances, than a direct solution of the classical optimal control problem.