Estimation and control of oscillators through short-range noisy proximity measurements

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.