Optimal Control System Synthesis Based on the Approximation of Extremals by Symbolic Regression

The article presents a solution to the optimal control synthesis problem based on the approximation of extremals. At the first stage it is proposed to solve the optimal control problem for various initial states, and at the second stage, to use the found optimal trajectories to determine the structure of the synthesizing function. Symbolic regression methods are used for approximation. Simulation is carried out for a car-like robot. The structure of the synthesizing function is found by the network operator method. A comparison of the solutions obtained using the synthesizing function found for the set of initial conditions with known solutions allows concluding that the proposed method is effective for the optimal control system synthesis.