Optimal Decentralized Control With Asymmetric One-Step Delayed Information Sharing

We consider optimal control of decentralized LQG problems for plants having nested subsystems controlled by two players with asymmetric information sharing patterns between them. In the main scenario, the players are assumed to have a unidirectional error-free, unlimited-rate communication channel with a unit delay in one direction and no communication in the other. A second model, presented for completeness, considers a channel with no delay in one direction and a unit delay in the other. Delayed information-sharing patterns do not, in general, admit linear optimal control laws and are thus difficult to control optimally. However, in these scenarios, we show that the problems have a partially nested information structure and, thus, linear optimal control laws exist. Summary statistics are identified and analytical solutions to the optimal control laws are derived. State and output feedback cases are solved for both scenarios.

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