Optimal control of nonlinear systems with separated linear part via quadratic criteria

We present a method for synthesis of optimal control with feedback of nonlinear systems with separated linear part via quadratic criteria. This method is based on a special method of successive approximations, which allows, under standard assumptions, to find optimal control within any finite time interval and to get the procedure of its construction. An example is provided for applying this method for synthesis of control of a system which is similar to Watt’s centrifugal governor.