White-noise-aided Control

TL;DR

This paper introduces a white-noise-aided control method that stabilizes perturbed systems more efficiently, reducing transient times and costs, with demonstrated effectiveness on a chaotic system and various noise types.

Contribution

It develops a noise-aiding stabilization approach for perturbed systems, proving its effectiveness and efficiency through theoretical analysis and numerical examples.

Findings

Noise-aided control stabilizes perturbed systems more effectively.

White noise reduces control transient times and costs.

Common noise is most efficient among various noise types.

Abstract

The issue of white-noise-aided control is considered and its availability is proved. And a noise-aiding way is developed to stabilize perturbed systems to be input-to-state stable (ISS) with respect to (w.r.t.) perturbations. To illustrate its effectiveness, the white-noise-aided control of a parameter perturbed chaotic Chen system is given as an example. And numerically, it shows that, comparing to the un-noise-aided case, noise-aided control can not only shorten the control's transient process but also save its cost. These are also demonstrated by various aiding noises such as common (symmetric) noise and non-common (independent or asymmetric) noise, where common noise is found to be the most efficient in enhancing the control.