  Standard H2 optimal control of networked dynamic systems tend to become
unscalable with network size. Structural constraints can be imposed on the
design to counteract this problem albeit at the risk of making the solution
non-convex. In this paper, we present a special class of structural constraints
such that the H2 design satisfies a quadratic invariance condition, and
therefore can be reformulated as a convex problem. This special class consists
of structured and weighted projections of the input and output spaces. The
choice of these projections can be optimized to match the closed-loop
performance of the reformulated controller with that of the standard H2
controller. The advantage is that unlike the latter, the reformulated
controller results in a hierarchical implementation which requires
significantly lesser number of communication links, while also admitting model
and controller reduction that helps the design to scale computationally. We
illustrate our design with simulations of a 500-node network.
