Error bounds for finite step approximations for solving infinite horizon controlled Markov set-chains

This note considers finite-step approximations for solving an infinite-horizon controlled Markov set-chain problem with finite state and action spaces. We develop a value-iteration type algorithm based on the optimality equation developed by Kurano et al. and analyze an error bound relative to the optimal value that satisfies the optimality equation from the successive approximation. We further analyze an error bound of the approximate control policy defined from a finite-step approximate value by applying the value-iteration type algorithm.