Optimal decentralized control in unidirectional one-step delayed sharing pattern

We consider an optimal decentralized LQG control problem for a plant with nested structure controlled by two players. Players are assumed to have a unidirectional one-step delayed error-free communication channel, i.e. there is a unit delay in information transmission in one direction and no transmission in the other direction. Full state feedback is assumed. Delayed information sharing patterns in general do not admit linear optimal control laws and are thus difficult to control optimally. However, in this scenario, we show that the problem has a partially nested information structure, and thus a linear optimal control law exists. Summary statistics to characterize this law are developed and a deterministic convex optimization problem is formulated whose solution yields the optimal control law.