Singular perturbation method applied to the open-loop discrete optimal control problem with two small parameters

Abstract

The open-loop optimal control of a linear, shift-invariant, singularly perturbed system with two small parameters is considered. The two small parameters are interrelated and approach zero simultaneously. The resulting two-point boundary value problem is put in the singularly perturbed form. A singular perturbation method is developed to obtain approximate solutions composed of an outer series, two initial correction series and two final correction series to recover the lost boundary conditions in the process of degeneration. An example is provided to illustrate the proposed method.