Noninvertibility and the structure of basins of attraction in a model adaptive control system

Raymond A. Adomaitis; Ioannis G. Kevrekidis

doi:10.1007/BF01209149

Noninvertibility and the structure of basins of attraction in a model adaptive control system

Raymond A. Adomaitis, Ioannis G. Kevrekidis

Chemical & Biological Engineering

Research output: Contribution to journal › Article › peer-review

29 Scopus citations

Abstract

We present a two-dimensional, nonlinear map, arising from a simple adaptive control problem, which exhibits disconnected boundaries separating the basins of attraction of its coexisting attractors. We perform a detailed study of the relation between this phenomenon and the noninvertible nature of the map and demonstrate how the complex basin structure is caused by a change in the number of preimages of points along a stable manifold.

Original language	English (US)
Pages (from-to)	95-105
Number of pages	11
Journal	Journal of Nonlinear Science
Volume	1
Issue number	1
DOIs	https://doi.org/10.1007/BF01209149
State	Published - Feb 1991

All Science Journal Classification (ASJC) codes

General Engineering
Applied Mathematics
Modeling and Simulation

Keywords

adaptive control
basins of attraction
bifurcations
noninvertibility

Access to Document

10.1007/BF01209149

Cite this

@article{8a2dc481cb9c49de8efa61181bc95519,

title = "Noninvertibility and the structure of basins of attraction in a model adaptive control system",

abstract = "We present a two-dimensional, nonlinear map, arising from a simple adaptive control problem, which exhibits disconnected boundaries separating the basins of attraction of its coexisting attractors. We perform a detailed study of the relation between this phenomenon and the noninvertible nature of the map and demonstrate how the complex basin structure is caused by a change in the number of preimages of points along a stable manifold.",

keywords = "adaptive control, basins of attraction, bifurcations, noninvertibility",

author = "Adomaitis, {Raymond A.} and Kevrekidis, {Ioannis G.}",

year = "1991",

month = feb,

doi = "10.1007/BF01209149",

language = "English (US)",

volume = "1",

pages = "95--105",

journal = "Journal of Nonlinear Science",

issn = "0938-8974",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - Noninvertibility and the structure of basins of attraction in a model adaptive control system

AU - Adomaitis, Raymond A.

AU - Kevrekidis, Ioannis G.

PY - 1991/2

Y1 - 1991/2

N2 - We present a two-dimensional, nonlinear map, arising from a simple adaptive control problem, which exhibits disconnected boundaries separating the basins of attraction of its coexisting attractors. We perform a detailed study of the relation between this phenomenon and the noninvertible nature of the map and demonstrate how the complex basin structure is caused by a change in the number of preimages of points along a stable manifold.

AB - We present a two-dimensional, nonlinear map, arising from a simple adaptive control problem, which exhibits disconnected boundaries separating the basins of attraction of its coexisting attractors. We perform a detailed study of the relation between this phenomenon and the noninvertible nature of the map and demonstrate how the complex basin structure is caused by a change in the number of preimages of points along a stable manifold.

KW - adaptive control

KW - basins of attraction

KW - bifurcations

KW - noninvertibility

UR - http://www.scopus.com/inward/record.url?scp=0001775901&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001775901&partnerID=8YFLogxK

U2 - 10.1007/BF01209149

DO - 10.1007/BF01209149

M3 - Article

AN - SCOPUS:0001775901

SN - 0938-8974

VL - 1

SP - 95

EP - 105

JO - Journal of Nonlinear Science

JF - Journal of Nonlinear Science

IS - 1

ER -

Noninvertibility and the structure of basins of attraction in a model adaptive control system

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this