  We propose in the paper a novel framework for using a common control input to
simultaneously steer an infinite ensemble of networked control systems. We
address the problem of co-designing information flow topology and network
dynamics of every individual networked system so that a continuum ensemble of
such systems is controllable. To keep the analysis tractable, we focus in the
paper on a special class of ensembles systems, namely ensembles of multi-agent
formation systems. Specifically, we consider an ensemble of formation systems
indexed by a parameter in a compact, real analytic manifold. Every individual
formation system in the ensemble is composed of $N$ agents. These agents evolve
in $\mathbb{R}^n$ and can access relative positions of their neighbors. The
information flow topology within every individual formation system is, by
convention, described by a directed graph where the vertices correspond to the
$N$ agents and the directed edges indicate the information flow. For
simplicity, we assume in the paper that all the individual formation systems
share the same information flow topology described by a common digraph $G$.
Amongst other things, we establish a sufficient condition for approximate
path-controllability of the continuum ensemble of formation systems. We show
that if the digraph $G$ is strongly connected and the number $N$ of agents in
each individual system is great than $(n + 1)$, then every such system in the
ensemble is simultaneously approximately path-controllable over a
path-connected, open dense subset.
