  This paper deals with control of partially observable discrete-time
stochastic systems. It introduces and studies Markov Decision Processes with
Incomplete Information and with semi-uniform Feller transition probabilities.
The important feature of these models is that their classic reduction to
Completely Observable Markov Decision Processes with belief states preserves
semi-uniform Feller continuity of transition probabilities. Under mild
assumptions on cost functions, optimal policies exist, optimality equations
hold, and value iterations converge to optimal values for these models. In
particular, for Partially Observable Markov Decision Processes the results of
this paper imply new and generalize several known sufficient conditions on
transition and observation probabilities for weak continuity of transition
probabilities for Markov Decision Processes with belief states, the existence
of optimal policies, validity of optimality equations defining optimal
policies, and convergence of value iterations to optimal values.
