Beyond partial control: Controlling chaotic transients with the safety function

TL;DR

This paper introduces a control strategy that uses a safety function to steer chaotic orbits into a safe set, transforming it into a global attractor and enhancing control over transient chaos.

Contribution

It develops a novel control method that gradually guides chaotic trajectories into a safe set, extending partial control to full attraction using the safety function.

Findings

The safety function effectively guides chaotic orbits to the safe set.

The safe set can be converted into a global attractor.

The method reduces the control effort needed for stabilization.

Abstract

Partial control is a technique used in systems with transient chaos. The aim of this control method is to avoid the escape of the orbits from a region Q of the phase space where the transient chaotic dynamics takes place. This technique is based on finding a special subset of Q called the safe set. The chaotic orbit can be sustained in the safe set with a minimum amount of control. In this work we develop a control strategy to gradually lead any chaotic orbit in Q to the safe set by using the safety function. With the technique proposed here, the safe set can be converted into a global attractor of Q.