Optimal decentralized control in unidirectional one-step delayed sharing pattern with partial output feedback

We consider optimal decentralized LQG control for a plant with nested structure controlled by two players receiving partial output observations from the plant. A unidirectional one-step delayed error-free communication channel is assumed to exist between the two players, i.e., there is a unit delay in information transmission in one direction and no transmission in the other direction. One of the players has access to a subset of state variables while the other can only observe a noisy output. We show that the problem has a partially nested information structure, and thus a linear optimal control law exists. Using summary statistics, the computation of the optimal law is made tractable and a deterministic convex optimization problem is formulated whose solution yields the optimal control law.