This paper deals with asymptotic optimality of a stochastic dynamic system driven by a singularly perturbed Markov chain with finite state space. The states of the Markov chain belong to several groups such that transitions among the states within each group occur much more frequently than the transitions among the states in different groups. Aggregating the states of the Markov chain leads to a limit control problem which is obtained by replacing the states in each group by the corresponding average distribution. The limit control problem is simpler to solve as compared with the original one. A nearly optimal solution for the original problem is constructed by using the optimal solution to the limit problem. To demonstrate, the suggested approach of asymptotic optimal control is applied to manufacturing systems of production planning examples.
Paru en septembre 1996 , 29 pages