Further progress in partial control of chaotic systems

Juan Sabuco, Miguel Sanjuan, Samuel Zambrano

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

The Partial Control technique is a new paradigm in the control of chaotic systems in the presence of noise. This new approach of control allows one to keep trajectories of a dynamical system inside a region from which nearly all the trajectories diverge. Its main advantage is that this goal is achieved even if the corrections applied to the trajectories (control) are smaller than the action of environmental disturbances (noise) on the dynamics. This is a rather counterintuitive result, that is achieved thanks to what we call safe sets. Here, we study the use of the Partial Control technique in one of the most famous chaotic maps, the Hˇznon map, and the deep relationship between the safe sets and the sets of points with different escape times, the escape time sets. We also show how it is possible to find certain extended safe sets that can be used instead of the safe sets in the Partial Control technique. We also discuss briefly the development of a new algorithm to find these new safe sets in any dynamical system with a chaotic behaviour.

Original languageEnglish
Title of host publicationChaos, CNN, Memristors and Beyond: A Festschrift for Leon Chua
PublisherWorld Scientific Publishing Co.
Pages393-403
Number of pages11
ISBN (Electronic)9789814434805
ISBN (Print)9789814434799
DOIs
Publication statusPublished - Jan 1 2013

ASJC Scopus subject areas

  • Computer Science(all)
  • Mathematics(all)

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