Solution of the Problem of the Control System General Synthesis by Approximation of a Set of Extremals

The problem of the control system general synthesis is considered. This problem in general case requires finding the solution in the form of multidimensional function of a vector argument. Placing this control function into the right-hand part of differential equations of the control object model allows receiving the system of differential equations which partial solution from any initial condition of the given set is always optimal trajectory for the given quality criterion. In this paper, the problem of control general synthesis is solved based on the approximation of the set of optimal control problem solutions for different initial conditions. These solutions are called extremals. Previously, to solve the general synthesis problem, symbolic regression methods were used without approximation of extremals. Therefore it was often impossible to estimate the proximity of the found solution to the optimal one. To avoid this issue in this work initially we solve the optimal control problems for different initial conditions, and then these solutions are approximated by the symbolic regression method. In a presented computational experiment the proposed approach is used to solve the problem of the control system general synthesis for the mobile robot moving in the area with obstacles. © 2020, Springer Nature Switzerland AG.