A separation result for nested dynamic decentralized LQG problems

In a nested decentralized LQG control problem, if the control variable u depends on the random vector y, then the expected value of the system´s current state given y may not (unlike the centralized problem) be a sufficiently detailed summary of y to use to compute the optimal u. This paper describes a method for finding a small number of functions of y sufficient for computing the optimal u, yielding a result very similar to the separation of estimation and control discussed in [1]. In particular we obtain for a class of decentralized problems the analogues of the type of recursive off-line and on-line computation found in the (centralized) Kalman-Bucy filter. A detailed exposition appears in [2].