Machine Learning Control by Symbolic Regression for the Extended Optimal Control Problem of Robot Group

The extended optimal control problem is considered. In the problem, it is necessary to find such an optimal control function so that it not only solves the optimal control problem, that is, it ensures the achievement of the terminal state with the optimal value of the quality criterion for the considered mathematical model of the control object under consideration, but and this control function was implemented in the control system of the real object. This means that the control function should depend on the vector of the state space, and the optimal solution must retain the property of optimality under small perturbations of the found solution. To solve this problem machine learning control by symbolic regression is used. In the extended optimal control problem, the problem statement of stabilization system synthesis for movement along the optimal trajectory is included. Solving the synthesis problem is performed by symbolic regression, the network operator method. At the solving the synthesis problem a domain of initial conditions is considered instead of one point of initial state. This provides small sensitivity found solution to perturbations of initial states. The example of solving the extended optimal control problem with phase constraints for two quadcopters is presented.