  We consider distributed control of double-integrator networks, where agents
are subject to stochastic disturbances. We study performance of such networks
in terms of coherence, defined through an H2 norm metric that represents the
variance of nodal state fluctuations. Specifically, we address known
performance limitations of the standard consensus protocol, which cause this
variance to scale unboundedly with network size for a large class of networks.
We propose distributed proportional integral (PI) and proportional derivative
(PD) controllers that relax these limitations and achieve bounded variance, in
cases where agents can access an absolute measurement of one of their states.
This case applies to, for example, frequency control of power networks and
vehicular formation control with limited sensing. We discuss optimal tuning of
the controllers with respect to network coherence and demonstrate our results
in simulations.
