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Feedback control of the sine-Gordon antikink. / Porubov, A. V.; Fradkov, A. L.; Andrievsky, B. R.; Bondarenkov, R. S.
в: Wave Motion, Том 65, 09.2016, стр. 147-155.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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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