A functional expansion approach to the solution of nonlinear feedback systems

This paper presents two results: (i) a new structure for the solution of nonlinear analytic systems, and (ii) an application of Bellman's Fundamental Technique to obtain the sub-optimal-feedback control of a class of quasilinear systems with non-quadratic performance indices. The application of the Fundamental Technique with a non-linear auxiliary equation is shown to result in higher order approximating equations which are linear. Using the method by separation of variables, two examples are solved.