Control System Synthesis Based on Optimal Trajectories Approximation by Symbolic Regression for Group of Robots*

The paper considers the solution of the problem of optimal control system synthesis. It is proposed to solve this problem based on the approximation of the set of optimal trajectories using symbolic regression methods. At the first step the optimal control problem is solved for various initial states; at the second step symbolic regression method is used to approximate the obtained set of optimal trajectories. In the suggested approach the proximity of the solution to the optimal one is determined by the accuracy of the approximation. A computational experiment of solving the applied problem of optimal control system synthesis for a group of car-like mobile robots in space with dynamic and static phase constraints is presented. The experiment showed that the found synthesized control function allows to move robots by the trajectory close to the optimal one for any initial state from a given domain.