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 -