  In this paper, we investigate a decentralized control problem with nested
subsystems, which is a general model for one-directional communication amongst
many subsystems. The noises in our dynamics are modelled as uncertain variables
which take values in finite sets. The objective is to minimize a worst-case
shared cost. We demonstrate how the prescription approach can simplify the
information structure and derive a structural form for optimal control
strategies. The structural form allows us to restrict attention to control
strategies whose domains do not grow in size with time, and thus, this form can
be utilized in systems with long time horizons. Finally, we present a dynamic
program to derive the optimal control strategies and validate our results with
a numerical example.
