Optimal Decentralized Control with Asymmetric One-Step Delayed Information Sharing

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.