A functional expansion approach to the solution of nonlinear feedback problems

The application of a functional expansion technique introduced by Bellman to the determination of nonlinear optimal control laws is described. For a certain class of "smooth" control problems, it is demonstrated that the expansion technique may be improved by use of a nonlinear (rather than linear) auxiliary equation which is based on a known cost-to-go function for an associated "linear-quadratic" optimal control problem.