Risk Sensitive Control of Finite State Machines on an Infinite Horizon I

In this paper we consider robust and risk sensitive control of discrete time finite state systems on an infinite horizon. The solution of the state feedback robust control problem is characterized in terms of the value of an average cost dynamic game. The risk sensitive stochastic optimal control problem is solved using the policy iteration algorithm, and the optimal rate is expressed in terms of the value of a stochastic dynamic game with average cost per unit time criterion. By taking a small noise limit a deterministic dynamic game is obtained, which is closely related to the robust control problem. 1 Introduction. There are various approaches to treating disturbances in control systems. In stochastic control, disturbances are modelled as stochastic processes (random noise). On the other hand, in H1 /robust control theory disturbances are modelled deterministically. The theory of risk sensitive optimal control provides a link between stochastic and deterministic approaches. The l..