| 引用本文: | 郭春丽,胡蓉.反阻尼一维波动方程的稳定性(英文)[J].控制理论与应用,2022,39(11):2161~2167.[点击复制] |
| GUO Ghun-li,HU Rong.Stabilization of a 1-D wave equation with anti-damping[J].Control Theory and Technology,2022,39(11):2161~2167.[点击复制] |
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| 反阻尼一维波动方程的稳定性(英文) |
| Stabilization of a 1-D wave equation with anti-damping |
| 摘要点击 1200 全文点击 306 投稿时间：2021-09-15 修订日期：2022-11-03 |
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| DOI编号 10.7641/CTA.2022.10869 |
| 2022,39(11):2161-2167 |
| 中文关键词 波动方程 边界控制 稳定性 |
| 英文关键词 wave equation boundary control stability |
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| 中文摘要 |
| 文章利用边界控制法研究了一类反阻尼一维波动方程的稳定性. 首先, 通过边界控制的backstepping方法, 引入
包含有两个核函数的积分变换, 将控制系统转化为稳定的目标系统. 核函数个数的增加导致核函数方程更加复杂, 文中
运用了一系列的数学计算技巧求解出核函数, 从而得到反馈控制器; 其次, 运用类似的方法找到变换的逆变换; 最后, 选
择合适范数, 利用变换及逆变换的有界性证明得到闭环系统的稳定性. |
| 英文摘要 |
| This paper is to stabilize a 1-D wave equation with an anti-damping by boundary control. To use the backstepping
method of boundary control, a new transformation of two kernel functions is introduced. The equations of kernel
functions are more complicated mathematically. By some mathematical skill, solutions of the kernel equations are
constructed. Finally, the inverse transformation is attained. Through boundedness of the transformation and its inverse,
stability of the closed-loop system is established. |
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