Stabilizing multiple equilibria and cycles with noisy prediction-based control

TL;DR

This paper investigates how noise can be used to stabilize multiple equilibria and cycles in non-smooth maps through prediction-based control, providing conditions for global stabilization and analyzing the effect of noise on control intensity.

Contribution

It introduces new sufficient conditions for global stabilization of multiple equilibria using noisy prediction-based control in non-smooth maps.

Findings

Noise relaxes restrictions on control intensity.

Control can be decreased with the addition of noise.

Numerical verification supports theoretical results.

Abstract

Pulse stabilization of cycles with Prediction-Based Control including noise and stochastic stabilization of maps with multiple equilibrium points is analyzed for continuous but, generally, non-smooth maps. Sufficient conditions of global stabilization are obtained. Introduction of noise can relax restrictions on the control intensity. We estimate how the control can be decreased with noise and verify it numerically.