Feedback control modulation for controlling chaotic maps
Articles
Roberta Hansen
Universidad de Buenos Aires
https://orcid.org/0000-0002-4805-5241
Graciela A. González
Universidad de Buenos Aires,
https://orcid.org/0000-0002-9240-2132
Published 2021-05-01
https://doi.org/10.15388/namc.2021.26.23052
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Keywords

chaos control
proportional feedback control
delayed feedback control
parameter modulation
control of hyperchaos

How to Cite

Hansen R. and González G. A. (2021) “Feedback control modulation for controlling chaotic maps”, Nonlinear Analysis: Modelling and Control, 26(3), pp. 419-439. doi: 10.15388/namc.2021.26.23052.

Abstract

Based on existing feedback control methods such as OGY and Pyragas, alternative new schemes are proposed for stabilization of unstable periodic orbits of chaotic and hyperchaotic dynamical systems by suitable modulation of a control parameter. Their performances are improved with respect to: (i) robustness, (ii) rate of convergences, (iii) reduction of waiting time, (iv) reduction of noise sensitivity. These features are analytically investigated, the achievements are rigorously proved and supported by numerical simulations. The proposed methods result successful for stabilizing unstable periodic orbits in some classical discrete maps like 1-D logistic and standard 2-D Hénon, but also in the hyperchaotic generalized n-D Hénon-like maps.

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