Boundary Energy Control of the Sine-Gordon Equation*

The boundary energy control problem for the sine-Gordon equation is posed. Two control laws solving this problem based on 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 algorithms demonstrate attainability of the control goal both for the cases of decreasing and increasing the system energy and show high rate of vanishing of the control error.