Cheap control for a class of nonlinear system

A quadratic regulator problem for a class of nonlinear system, in which a small parameter multiplies the control cost, is considered. In the analysis of the problem, we utilize the method of multiple time-scale decomposition which has been devised for analyzing complex linear cheap control problems. In so doing, we extend the class of nonlinear systems, considerably, for which the minimum cost becomes zero as the small parameter goes to zero.