Generating chaos via feedback control from a stable TS fuzzy system through a sinusoidal nonlinearity

Zhong Li; Jin Bae Park; Guanrong Chen; Young Hoon Joo; Yoon Ho Choi

doi:10.1142/S0218127402005844

Generating chaos via feedback control from a stable TS fuzzy system through a sinusoidal nonlinearity

Zhong Li, Jin Bae Park, Guanrong Chen, Young Hoon Joo, Yoon Ho Choi

Department of Electrical and Electronic Engineering

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

14 Citations (Scopus)

Abstract

An approach is proposed for making chaotic a given stable Takagi-Sugeno (TS) fuzzy system using state feedback control of arbitrarily small magnitude. The feedback controller chosen among several candidates is a simple sinusoidal function of the system states, which can lead to uniformly bounded state vectors of the controlled system with positive Lyapunov exponents, and satisfy the chaotic mechanisms of stretching and folding, thereby yielding chaotic dynamics. This approach is mathematically proven for rigorous generation of chaos from a stable TS fuzzy system, where the chaos is in the sense of Li and Yorke. A numerical example is included to visualize the theoretical analysis and the controller design.

Original language	English
Pages (from-to)	2283-2291
Number of pages	9
Journal	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume	12
Issue number	10
DOIs	https://doi.org/10.1142/S0218127402005844
Publication status	Published - 2002 Oct

All Science Journal Classification (ASJC) codes

Modelling and Simulation
Engineering (miscellaneous)
General
Applied Mathematics

Access to Document

10.1142/S0218127402005844

Cite this

@article{9ed7fc0a6a6b4aa4a17861f568b0d0f9,

title = "Generating chaos via feedback control from a stable TS fuzzy system through a sinusoidal nonlinearity",

abstract = "An approach is proposed for making chaotic a given stable Takagi-Sugeno (TS) fuzzy system using state feedback control of arbitrarily small magnitude. The feedback controller chosen among several candidates is a simple sinusoidal function of the system states, which can lead to uniformly bounded state vectors of the controlled system with positive Lyapunov exponents, and satisfy the chaotic mechanisms of stretching and folding, thereby yielding chaotic dynamics. This approach is mathematically proven for rigorous generation of chaos from a stable TS fuzzy system, where the chaos is in the sense of Li and Yorke. A numerical example is included to visualize the theoretical analysis and the controller design.",

author = "Zhong Li and Park, {Jin Bae} and Guanrong Chen and Joo, {Young Hoon} and Choi, {Yoon Ho}",

year = "2002",

month = oct,

doi = "10.1142/S0218127402005844",

language = "English",

volume = "12",

pages = "2283--2291",

journal = "International Journal of Bifurcation and Chaos in Applied Sciences and Engineering",

issn = "0218-1274",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "10",

}

TY - JOUR

T1 - Generating chaos via feedback control from a stable TS fuzzy system through a sinusoidal nonlinearity

AU - Li, Zhong

AU - Park, Jin Bae

AU - Chen, Guanrong

AU - Joo, Young Hoon

AU - Choi, Yoon Ho

PY - 2002/10

Y1 - 2002/10

N2 - An approach is proposed for making chaotic a given stable Takagi-Sugeno (TS) fuzzy system using state feedback control of arbitrarily small magnitude. The feedback controller chosen among several candidates is a simple sinusoidal function of the system states, which can lead to uniformly bounded state vectors of the controlled system with positive Lyapunov exponents, and satisfy the chaotic mechanisms of stretching and folding, thereby yielding chaotic dynamics. This approach is mathematically proven for rigorous generation of chaos from a stable TS fuzzy system, where the chaos is in the sense of Li and Yorke. A numerical example is included to visualize the theoretical analysis and the controller design.

AB - An approach is proposed for making chaotic a given stable Takagi-Sugeno (TS) fuzzy system using state feedback control of arbitrarily small magnitude. The feedback controller chosen among several candidates is a simple sinusoidal function of the system states, which can lead to uniformly bounded state vectors of the controlled system with positive Lyapunov exponents, and satisfy the chaotic mechanisms of stretching and folding, thereby yielding chaotic dynamics. This approach is mathematically proven for rigorous generation of chaos from a stable TS fuzzy system, where the chaos is in the sense of Li and Yorke. A numerical example is included to visualize the theoretical analysis and the controller design.

UR - http://www.scopus.com/inward/record.url?scp=0036815823&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036815823&partnerID=8YFLogxK

U2 - 10.1142/S0218127402005844

DO - 10.1142/S0218127402005844

M3 - Article

AN - SCOPUS:0036815823

SN - 0218-1274

VL - 12

SP - 2283

EP - 2291

JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

IS - 10

ER -

Generating chaos via feedback control from a stable TS fuzzy system through a sinusoidal nonlinearity

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this