On the nonlinear regulator problem

A new method is presented to obtain a state feedback form solution to an optimal control problem with nonlinear dynamics and a quadratic performance index. The method is based on solving an integral equation equivalent to the two-point boundary-value problem related to the optimization problem by applying an inverse theorem concerning analytic nonlinear operators. Compared with the previous methods, this one is straightforward, more generally applicable, and gives important additional knowledge about the solution. An example is presented to illustrate the use of the method.