Singular perturbation method applied to the open‐loop discrete optimal control problem

The open‐loop optimal control of a linear, shift‐invariant, singularly perturbed discrete system is considered. The resulting two‐point boundary value problem (TPBVP) is cast in the singularly perturbed form. It is found that in the process of degeneration, the original system loses some of the initial and final conditions. A singular perturbation method is developed to obtain approximate solutions composed of outer series, initial correction series and final correction series to recover the lost boundary conditions. The method is given for zeroth, first and any order of approximation. An example is provided to illustrate the proposed method.