Better stability with measurement errors

TL;DR

This paper shows that, counterintuitively, introducing a specific amount of measurement error in feedback control systems can enhance their stability, supported by diverse numerical examples across multiple fields.

Contribution

It reveals that measurement errors can improve system stability, challenging the conventional belief that more precise measurements always lead to better control.

Findings

Measurement error can enhance stability in feedback systems.

Numerical examples demonstrate improved control in various applications.

Counterintuitive role of measurement noise in system stabilization.

Abstract

Often it is desirable to stabilize a system around an optimal state. This can be effectively accomplished using feedback control, where the system deviation from the desired state is measured in order to determine the magnitude of the restoring force to be applied. Contrary to conventional wisdom, i.e. that a more precise measurement is expected to improve the system stability, here we demonstrate that a certain degree of measurement error can improve the system stability. We exemplify the implications of this finding with numerical examples drawn from various fields, such as the operation of a temperature controller, the confinement of a microscopic particle, the localization of a target by a microswimmer, and the control of a population.