Optimal stabilization of unstable periodic orbits embedded in chaotic systems

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Main Author: C.A. Cruz-Villar
Format: Artículo científico
Language:en
Published: Sociedad Mexicana de Física A.C. 2007
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author C.A. Cruz-Villar
author_facet C.A. Cruz-Villar
contents Optimal stabilization of unstable periodic orbits embedded in chaotic systems C.A. Cruz-Villar Física, Astronomía y Matemáticas gradient flow sensitivity theory Optimal stabilization unstable periodic orbits A gradient-flow-based approach is proposed in this paper for stabilizing unstable periodic orbits (UPO) embedded in chaotic systems. Inorder to obtain an on-line stabilizing solution, the stabilization problem is considered to be an optimal control problem, and system statesensitivities with respect to the control input are introduced. The resulting feedback controller is able to stabilize UPO embedded in bothkind of systems, with or without an odd Floquet number. Moreover, the proposed approach is easily extended to identifying the period of theUPO to be stabilized when it is unknown. Simulation experiments of the proposed controller are carried out on the R¨ossler and the Lorenzsystems. 2007 artículo científico 0035-001X https://www.redalyc.org/articulo.oa?id=57053513 en http://www.redalyc.org/revista.oa?id=570 Revista Mexicana de Física application/pdf Sociedad Mexicana de Física A.C. Revista Mexicana de Física (México) Num.5 Vol.53
format Artículo científico
id redalyc_57053513
institution Redalyc
language en
publishDate 2007
publisher Sociedad Mexicana de Física A.C.
spellingShingle Optimal stabilization of unstable periodic orbits embedded in chaotic systems
C.A. Cruz-Villar
Física, Astronomía y Matemáticas
gradient flow
sensitivity theory
Optimal stabilization
unstable periodic orbits
Optimal stabilization of unstable periodic orbits embedded in chaotic systems C.A. Cruz-Villar Física, Astronomía y Matemáticas gradient flow sensitivity theory Optimal stabilization unstable periodic orbits A gradient-flow-based approach is proposed in this paper for stabilizing unstable periodic orbits (UPO) embedded in chaotic systems. Inorder to obtain an on-line stabilizing solution, the stabilization problem is considered to be an optimal control problem, and system statesensitivities with respect to the control input are introduced. The resulting feedback controller is able to stabilize UPO embedded in bothkind of systems, with or without an odd Floquet number. Moreover, the proposed approach is easily extended to identifying the period of theUPO to be stabilized when it is unknown. Simulation experiments of the proposed controller are carried out on the R¨ossler and the Lorenzsystems. 2007 artículo científico 0035-001X https://www.redalyc.org/articulo.oa?id=57053513 en http://www.redalyc.org/revista.oa?id=570 Revista Mexicana de Física application/pdf Sociedad Mexicana de Física A.C. Revista Mexicana de Física (México) Num.5 Vol.53
title Optimal stabilization of unstable periodic orbits embedded in chaotic systems
topic Física, Astronomía y Matemáticas
gradient flow
sensitivity theory
Optimal stabilization
unstable periodic orbits
url https://www.redalyc.org/articulo.oa?id=57053513