BOUNDARY VALUE PROBLEM FOR A THREE-TIME-SCALE SINGULARLY PERTURBED DISCRETE SYSTEM

摘要

In this paper, we consider a three time scale state model arising in the open- loop optimal control of singularly perturbed discrete systems. The perturbation method is described to solve a two point boundary value problem exhibiting boundary layer behavior at the initial and final points. We give conditions that guarantee existence and uniqueness of the solution, we achieve model order reduction and remove the time scale. A convergent iterative algorithm is provided to compute asymptotic approximations without need to use boundary layer correction terms as for the singular perturbation method.