Decentralized LQG control of systems with a broadcast architecture

In this paper, we consider dynamical subsystems interconnected in a broadcast architecture. In the broadcast-out case, the root node can affect several leaf nodes, but the leaf nodes do not affect any other nodes. Each subsystem is locally controlled via output feedback, and the controllers can communicate according to a structure that parallels the dynamic coupling between subsystems. Explicit state-space realizations for the optimal controllers are derived using a spectral factorization approach. An interpretation of the controller states is also provided in terms of optimal state estimators. We also address the dual broadcast-in case, where there is a single leaf node affected by multiple root nodes.