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

## TL;DR

This paper introduces a novel estimation and control method for balancing oscillator formations on a circle using only noisy, short-range proximity measurements, overcoming connectivity challenges.

## Contribution

It combines interval analysis-based estimation with a bang-bang controller to achieve formation balance despite measurement limitations.

## Key findings

- Formation can be balanced with tunable accuracy.
- The strategy is effective under noisy, short-range measurements.
- Numerical simulations validate the approach.

## Abstract

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.