  In this paper, we investigate a worst-case-scenario control problem with a
partially observed state. We consider a non-stochastic formulation, where
noises and disturbances in our dynamics are uncertain variables which take
values in finite sets. In such problems, the optimal control strategy can be
derived using a dynamic program (DP) with respect to the memory. The
computational complexity of this DP can be improved using a conditional range
of the state instead of the memory. We present a more general definition of an
information state which is sufficient to construct a DP without loss of
optimality, and show that the conditional range is an example of an information
state. Next, we extend this notion to define an approximate information state
and an approximate DP. We also bound the maximum loss of optimality when using
an approximate DP to derive the control strategy. Finally, we illustrate our
results in a numerical example.
