  A group behavior of a heterogeneous multi-agent system is studied which obeys
an "average of individual vector fields" under strong couplings among the
agents. Under stability of the averaged dynamics (not asking stability of
individual agents), the behavior of heterogeneous multi-agent system can be
estimated by the solution to the averaged dynamics. A following idea is to
"design" individual agent's dynamics such that the averaged dynamics performs
the desired task. A few applications are discussed including estimation of the
number of agents in a network, distributed least-squares or median solver,
distributed optimization, distributed state estimation, and robust
synchronization of coupled oscillators. Since stability of the averaged
dynamics makes the initial conditions forgotten as time goes on, these
algorithms are initialization-free and suitable for plug-and-play operation. At
last, nonlinear couplings are also considered, which potentially asserts that
enforced synchronization gives rise to an emergent behavior of a heterogeneous
multi-agent system.
