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Boundary Energy Control of the Sine-Gordon Equation * * This work was performed in IPME RAS, supported by RSF (grant 14-29-00142).

机译:Sine-Gordon方程的边界能控制 * * 此工作是在IPME RAS中执行的,得到了​​以下支持RSF(拨款14-29-00142)。

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摘要

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.
机译:提出了正弦-戈登方程的边界能控制问题。提出了两种基于速度梯度法的具有平滑和非平滑目标函数的控制律。事实证明,通过非光滑目标函数获得的控制定律可在有限时间内将系统引导至任何所需的非零能级。所提出算法的数值评估结果表明,在减少和增加系统能量的情况下,控制目标都是可以实现的,并且控制误差的消失率很高。

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