  We consider optimal control of decentralized LQG problems for plants
controlled by two players having asymmetric information sharing patterns
between them. In one scenario, players are assumed to have a bidirectional
error-free, unlimited rate communication channel with no delay in one direction
and a unit delay in the other. In another scenario, the communication channel
is assumed to be unidirectional with a unit delay. Delayed information sharing
patterns in general do not admit linear optimal control laws and are thus
difficult to control optimally. However, in these scenarios, we show that the
problem has a partially nested information structure, and thus linear optimal
control laws exist. Summary statistics to characterize these laws are developed
and deterministic convex optimization problems are formulated whose solutions
yield the optimal control laws. The state feedback case is solved for both
scenarios and extended to output and partial output feedback in case of
bidirectional and unidirectional channels respectively.
