  An information based method for solving stochastic control problems with
partial observation has been proposed. First, the information-theoretic lower
bounds of the cost function has been analysed. It has been shown, under rather
weak assumptions, that reduction of the expected cost with closed-loop control
compared to the best open-loop strategy is upper bounded by non-decreasing
function of mutual information between control variables and the state
trajectory. On the basis of this result, an Information Based Control method
has been developed. The main idea of the IBC consists in replacing the original
control task by a sequence of control problems that are relatively easy to
solve and such that information about the state of the system is actively
generated. Two examples of the operation of the IBC are given. It has been
shown that the IBC is able to find the optimal solution without using dynamic
programming at least in these examples. Hence the computational complexity of
the IBC is substantially smaller than complexity of dynamic programming, which
is the main advantage of the proposed method.
