  In this paper, we present a novel estimation and control strategy to balance
a formation of discrete-time oscillators on a circle. We consider the case in
which each oscillator only gathers noisy proximity measurements, whose range is
lower than the desired spacing along the circle, implying total
disconnectedness of the balanced formation. These restrictions pose relevant
challenges that are overcome through the symbiotic combination of an estimator
that borrows tools from interval analysis and a three-level bang-bang
controller. We prove that the formation can be balanced, with an accuracy that
can be regulated by tuning a controller parameter. The effectiveness of the
proposed strategy is further illustrated through a set of numerical
simulations.
