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Feedback control of the sine-Gordon antikink. / Porubov, A. V.; Fradkov, A. L.; Andrievsky, B. R.; Bondarenkov, R. S.

In: Wave Motion, Vol. 65, 09.2016, p. 147-155.

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

Harvard

Porubov, AV, Fradkov, AL, Andrievsky, BR & Bondarenkov, RS 2016, 'Feedback control of the sine-Gordon antikink', Wave Motion, vol. 65, pp. 147-155. https://doi.org/10.1016/j.wavemoti.2016.04.014

APA

Porubov, A. V., Fradkov, A. L., Andrievsky, B. R., & Bondarenkov, R. S. (2016). Feedback control of the sine-Gordon antikink. Wave Motion, 65, 147-155. https://doi.org/10.1016/j.wavemoti.2016.04.014

Vancouver

Porubov AV, Fradkov AL, Andrievsky BR, Bondarenkov RS. Feedback control of the sine-Gordon antikink. Wave Motion. 2016 Sep;65:147-155. https://doi.org/10.1016/j.wavemoti.2016.04.014

Author

Porubov, A. V. ; Fradkov, A. L. ; Andrievsky, B. R. ; Bondarenkov, R. S. / Feedback control of the sine-Gordon antikink. In: Wave Motion. 2016 ; Vol. 65. pp. 147-155.

BibTeX

@article{6905eea626684a26ad693c033934f748,
title = "Feedback control of the sine-Gordon antikink",
abstract = "A new distributed speed-gradient feedback control algorithm for the sine-Gordon (SG) equation is proposed. It creates the antikink traveling wave mode for a broader class initial conditions compared to the uncontrolled system. In real physical problems it is difficult to provide consistent initial conditions for the second-order (in time) equations. Therefore for an uncontrolled system even small variations in the initial velocity relative to that of the exact antikink solution of the SG equation give rise to growing oscillations. The control algorithm allows one both to suppress defects and to obtain stable propagation of an antikink in the form of the exact traveling wave solution of the SG equation. In contrast to the existing algorithms the proposed algorithm does not require additional dissipative term for wave generation. (C) 2016 Elsevier B.V. All rights reserved.",
keywords = "Nonlinear wave, Feedback control, Nonlinear equation, Numerical solution, EQUATION, STABILIZATION, WAVES, MODEL",
author = "Porubov, {A. V.} and Fradkov, {A. L.} and Andrievsky, {B. R.} and Bondarenkov, {R. S.}",
year = "2016",
month = sep,
doi = "10.1016/j.wavemoti.2016.04.014",
language = "Английский",
volume = "65",
pages = "147--155",
journal = "Wave Motion",
issn = "0165-2125",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Feedback control of the sine-Gordon antikink

AU - Porubov, A. V.

AU - Fradkov, A. L.

AU - Andrievsky, B. R.

AU - Bondarenkov, R. S.

PY - 2016/9

Y1 - 2016/9

N2 - A new distributed speed-gradient feedback control algorithm for the sine-Gordon (SG) equation is proposed. It creates the antikink traveling wave mode for a broader class initial conditions compared to the uncontrolled system. In real physical problems it is difficult to provide consistent initial conditions for the second-order (in time) equations. Therefore for an uncontrolled system even small variations in the initial velocity relative to that of the exact antikink solution of the SG equation give rise to growing oscillations. The control algorithm allows one both to suppress defects and to obtain stable propagation of an antikink in the form of the exact traveling wave solution of the SG equation. In contrast to the existing algorithms the proposed algorithm does not require additional dissipative term for wave generation. (C) 2016 Elsevier B.V. All rights reserved.

AB - A new distributed speed-gradient feedback control algorithm for the sine-Gordon (SG) equation is proposed. It creates the antikink traveling wave mode for a broader class initial conditions compared to the uncontrolled system. In real physical problems it is difficult to provide consistent initial conditions for the second-order (in time) equations. Therefore for an uncontrolled system even small variations in the initial velocity relative to that of the exact antikink solution of the SG equation give rise to growing oscillations. The control algorithm allows one both to suppress defects and to obtain stable propagation of an antikink in the form of the exact traveling wave solution of the SG equation. In contrast to the existing algorithms the proposed algorithm does not require additional dissipative term for wave generation. (C) 2016 Elsevier B.V. All rights reserved.

KW - Nonlinear wave

KW - Feedback control

KW - Nonlinear equation

KW - Numerical solution

KW - EQUATION

KW - STABILIZATION

KW - WAVES

KW - MODEL

U2 - 10.1016/j.wavemoti.2016.04.014

DO - 10.1016/j.wavemoti.2016.04.014

M3 - статья

VL - 65

SP - 147

EP - 155

JO - Wave Motion

JF - Wave Motion

SN - 0165-2125

ER -

ID: 13719916