Analytical and Numerical Investigation for the Problem of Optimal Control of Nonlinear System via Quadratic Criteria

We present a method for synthesis of optimal control with feedback of some class of nonlinear systems via quadratic criteria. This method is based on a special method of successive approximations, whose convergence allows to prove an existence of optimal control and to get the procedure of its construction. The paper examines analytical and numerical investigation of the method and its realization by means of MathCloud system. It presents a numerical experiment to build optimal control of a physical pendulum.