Abstract
This paper studies a steady-state optimal control problem for nearly completely decomposable Markov chains. Using a singular perturbation approach, an aggregation method for the value determination equation is developed. The aggregation method is developed in three steps. First, a class of similarity transformations that transform the system into a singularly perturbed form is developed. Second, an aggregation method to compute the steady-state probability distribution is derived. Third, this aggregation method is applied to the value determination step of Howard's method.