Structural results for partially nested LQG systems over graphs

We identify a broad class of decentralized output-feedback LQG systems for which the optimal control strategies have a simple and intuitive estimation structure. We consider cases for which the coupling of dynamics among subsystems and the inter-controller communication are characterized by the same directed graph. For the class of graphs known as multitrees, we show that each controller need only estimate the states of the subsystems it affects (its descendants) as well as the subsystems it observes (its ancestors). The optimal control action for each controller is a linear function of the estimate it computes and the estimates computed by its ancestors. Moreover, all state estimates may be updated recursively, much like a Kalman filter.