This paper treats the infinite horizon discounted cost control problem for partially observable Markov decision processes. Sondik studied the class of finitely transient policies and showed that their value functions over an infinite time horizon are piecewise linear (p.w.l) and can be computed exactly by solving a system of linear equations. However, the condition for finite transience is stronger than is needed to ensure p.w.l. value functions. In this paper, we introduce alternatively the class of periodic policies whose value functions turn out to be also p.w.l. Moreover, we examine a more general condition than finite transience and periodicity that ensures p.w.l. value functions. We implement these ideas in a replacement problem under Markovian deterioration, investigate for periodic policies and give numerical examples.
OPTIMAL CONTROL FOR PARTIALLY OBSERVABLE MARKOV DECISION PROCESSES OVER AN INFINITE HORIZON