Beyond partial control: Controlling chaotic transients with the safety function

2021/05/06 by Rubén Capeáns, Miguel A. F. Sanjuán, Capeáns, Rubén +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Chaos control and synchronization #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems #math.DS #math.OC #nlin.CD

paper · pdf · doi:10.48550/arxiv.2105.03351

16 pages

arxiv created 2021/05/06 · arxiv updated 2021/09/06

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.

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• Controlling two-dimensional chaotic transients with the safety function

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