Robust Markov control processes

Abstract

We examine the average minimax control problem on a general state space with an unbounded cost function. The controller is uncertain about his model in the sense that he deals with a range of alternative models as possibly true. The aim of this paper is to establish the optimality inequality and to provide a minimax strategy for the controller. A new feature in our approach is an application of a generalised Tauberian relation that, in turn, allows us to impose relatively weak assumptions.