A Numerical Method for Solving Optimal Control Problems

A numerical method is developed for solving optimal control problems. There is realized an approach, so that an infinite-dimensional optimization problem is reduced to a finite-dimensional one, which is solved by a nonlinear programming method - the gravitation centers method (GCM). By applying GCM we find an optimal control, which can be of an arbitrary structure. We can solve two-point boundary value problems by applying algorithmic tools of random sampling. At the same time with GCM we obtain an optimal solution with an admissible accuracy and minimal consumption of computer time. A numerical example illustrates the efficiency of the developed method for optimal control problems.