Algorithm for Finding Optimal Control for Problems with a Free Right Endpoint Based on Gradient Descent

This manuscript addresses the problem of finding optimal control for dynamic systems using the gradient descent method. A numerical algorithm is constructed to find the optimal control in problems with a free right endpoint of the trajectory. The accuracy and speed of the algorithm depend on the choice of the time interval partition size and the stopping conditions of the gradient descent method. A key feature of the proposed algorithm is its ability to generalize for problems of finding optimal control with various types of boundary conditions. The algorithm's operation is illustrated by the example of finding the optimal temperature in a chemical kinetics problem. Numerical simulations have shown an improvement in accuracy and convergence speed compared to existing methods.