On the policy iteration algorithm for nondegenerate controlled diffusions under the ergodic criterion

Abstract

The subject of this chapter is the policy iteration algorithm for nondegenerate controlled diffusions. The results parallel the ones in Meyn (IEEE Trans Automat Control 42:1663–1680, 1997) for discrete-time controlled Markov chains. The model in (Meyn, IEEE Trans Automat Control 42:1663–1680, 1997) uses norm-like running costs, while we opt for the milder assumption of near-monotone costs. Also, instead of employing a blanket Lyapunov stability hypothesis, we provide a characterization of the region of attraction of the optimal control.