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Exploring nonlinearity by feedback. / Fradkov, Alexander.

In: Physica D: Nonlinear Phenomena, Vol. 128, No. 2-4, 15.04.1999, p. 159-168.

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

Harvard

Fradkov, A 1999, 'Exploring nonlinearity by feedback', Physica D: Nonlinear Phenomena, vol. 128, no. 2-4, pp. 159-168. https://doi.org/10.1016/S0167-2789(98)00322-4

APA

Fradkov, A. (1999). Exploring nonlinearity by feedback. Physica D: Nonlinear Phenomena, 128(2-4), 159-168. https://doi.org/10.1016/S0167-2789(98)00322-4

Vancouver

Fradkov A. Exploring nonlinearity by feedback. Physica D: Nonlinear Phenomena. 1999 Apr 15;128(2-4):159-168. https://doi.org/10.1016/S0167-2789(98)00322-4

Author

Fradkov, Alexander. / Exploring nonlinearity by feedback. In: Physica D: Nonlinear Phenomena. 1999 ; Vol. 128, No. 2-4. pp. 159-168.

BibTeX

@article{9c7990d1a8774079b925743a2c8d4b1e,
title = "Exploring nonlinearity by feedback",
abstract = "The possibilities of studying nonlinear behavior of physical systems by small feedback action are discussed. Analytical bounds of possible system energy change by feedback are established. It is shown that for a 1-DOF nonlinear oscillator, the change of energy by feedback can reach the limit achievable for a linear oscillator by a harmonic (non-feedback) action. The results are applied to different physical problems: evaluating the amplitude of action leading to escape from a potential well; stabilizing unstable modes of a nonlinear oscillator (pendulum); using feedback testing signals in spectroscopy. These and related studies are united by similarity of their goals (examination possibilities and limitations for changing a system behavior by feedback) and by unified methodology borrowed from cybernetics (control science). They, therefore, constitute a part of physics which can be called cybemeticalphysics.",
keywords = "Control of oscillations and chaos, Hamiltonian systems, Nonlinear resonance",
author = "Alexander Fradkov",
note = "Funding Information: The author acknowledges support of the Russian Foundation for Basic Research (Grant 96-01-01151) and of the Dutch Organization for Pure Research (NWO). ",
year = "1999",
month = apr,
day = "15",
doi = "10.1016/S0167-2789(98)00322-4",
language = "English",
volume = "128",
pages = "159--168",
journal = "Physica D: Nonlinear Phenomena",
issn = "0167-2789",
publisher = "Elsevier",
number = "2-4",

}

RIS

TY - JOUR

T1 - Exploring nonlinearity by feedback

AU - Fradkov, Alexander

N1 - Funding Information: The author acknowledges support of the Russian Foundation for Basic Research (Grant 96-01-01151) and of the Dutch Organization for Pure Research (NWO).

PY - 1999/4/15

Y1 - 1999/4/15

N2 - The possibilities of studying nonlinear behavior of physical systems by small feedback action are discussed. Analytical bounds of possible system energy change by feedback are established. It is shown that for a 1-DOF nonlinear oscillator, the change of energy by feedback can reach the limit achievable for a linear oscillator by a harmonic (non-feedback) action. The results are applied to different physical problems: evaluating the amplitude of action leading to escape from a potential well; stabilizing unstable modes of a nonlinear oscillator (pendulum); using feedback testing signals in spectroscopy. These and related studies are united by similarity of their goals (examination possibilities and limitations for changing a system behavior by feedback) and by unified methodology borrowed from cybernetics (control science). They, therefore, constitute a part of physics which can be called cybemeticalphysics.

AB - The possibilities of studying nonlinear behavior of physical systems by small feedback action are discussed. Analytical bounds of possible system energy change by feedback are established. It is shown that for a 1-DOF nonlinear oscillator, the change of energy by feedback can reach the limit achievable for a linear oscillator by a harmonic (non-feedback) action. The results are applied to different physical problems: evaluating the amplitude of action leading to escape from a potential well; stabilizing unstable modes of a nonlinear oscillator (pendulum); using feedback testing signals in spectroscopy. These and related studies are united by similarity of their goals (examination possibilities and limitations for changing a system behavior by feedback) and by unified methodology borrowed from cybernetics (control science). They, therefore, constitute a part of physics which can be called cybemeticalphysics.

KW - Control of oscillations and chaos

KW - Hamiltonian systems

KW - Nonlinear resonance

UR - http://www.scopus.com/inward/record.url?scp=0346335853&partnerID=8YFLogxK

U2 - 10.1016/S0167-2789(98)00322-4

DO - 10.1016/S0167-2789(98)00322-4

M3 - Article

AN - SCOPUS:0346335853

VL - 128

SP - 159

EP - 168

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 2-4

ER -

ID: 88362144