Universal method of optimal control synthesis offers a versatile method for the synthesis of optimal controls provides a solution to the synthesis problem for the class of piecewise constant functions for Lagrangian dynamical systems, the shape of the control law depends only on the structure of the cost functional and does not depend on the structure of the existing system of generalized forces. The effectiveness of the method is confirmed by a minimum of computational costs, as well as the maximum rate of convergence and accuracy to achieve the desired trajectory in comparison with the known solution for example has become a test for testing various control methods for the synthesis problem of a simple pendulum.

Keywords: combined maximum principle, optimal control, mathematical pendulum