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In this two-part paper, we identify a broad class of decentralizedoutput-feedback LQG systems for which the optimal control strategies have asimple intuitive estimation structure and can be computed efficiently. Roughly,we consider the class of systems for which the coupling of dynamics amongsubsystems and the inter-controller communication is characterized by the samedirected graph. Furthermore, this graph is assumed to be a multitree, that is,its transitive reduction can have at most one directed path connecting eachpair of nodes. In this first part, we derive sufficient statistics that may beused to aggregate each controller's growing available information. Eachcontroller must estimate the states of the subsystems that it affects (itsdescendants) as well as the subsystems that it observes (its ancestors). Theoptimal control action for a controller is a linear function of the estimate itcomputes as well as the estimates computed by all of its ancestors. Moreover,these state estimates may be updated recursively, much like a Kalman filter.

Optimal Control for LQG Systems on Graphs---Part I: Structural Results