Research output: Contribution to journal › Article › peer-review
Boundary energy control of a system governed by the nonlinear Klein–Gordon equation. / Dolgopolik, Maksim; Fradkov, Alexander L.; Andrievsky, Boris.
In: Mathematics of Control, Signals, and Systems, Vol. 30, No. 1, 7, 01.03.2018.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Boundary energy control of a system governed by the nonlinear Klein–Gordon equation
AU - Dolgopolik, Maksim
AU - Fradkov, Alexander L.
AU - Andrievsky, Boris
PY - 2018/3/1
Y1 - 2018/3/1
N2 - The boundary energy control problem for the sine-Gordon and the nonlinear Klein–Gordon equations is posed. Two control laws solving this problem based on the speed-gradient method with smooth and nonsmooth goal functions are proposed. The control law obtained via a nonsmooth goal function is proved to steer the system to any required nonzero energy level in finite time. The results of the numerical evaluation of the proposed algorithm for an undamped nonlinear elastic string demonstrate attainability of the control goal for the cases of both decreasing and increasing systems’ energy and show high rate of vanishing of the control error.
AB - The boundary energy control problem for the sine-Gordon and the nonlinear Klein–Gordon equations is posed. Two control laws solving this problem based on the speed-gradient method with smooth and nonsmooth goal functions are proposed. The control law obtained via a nonsmooth goal function is proved to steer the system to any required nonzero energy level in finite time. The results of the numerical evaluation of the proposed algorithm for an undamped nonlinear elastic string demonstrate attainability of the control goal for the cases of both decreasing and increasing systems’ energy and show high rate of vanishing of the control error.
KW - Energy control
KW - Klein–Gordon equation
KW - Sine-Gordon equation
KW - Speed-gradient method
UR - http://www.scopus.com/inward/record.url?scp=85047226904&partnerID=8YFLogxK
U2 - 10.1007/s00498-018-0213-5
DO - 10.1007/s00498-018-0213-5
M3 - Article
AN - SCOPUS:85047226904
VL - 30
JO - Mathematics of Control, Signals, and Systems
JF - Mathematics of Control, Signals, and Systems
SN - 0932-4194
IS - 1
M1 - 7
ER -
ID: 37786501