In this paper, we are interested in stabilizing a nonlinear axially moving string by an adaptive boundary control. The existence and uniqueness of a solution of the closed loop system is dealt with in the framework of the nonlinear semigroup theory by using a theorem due to Crandall-Liggett. The control is constructed through a low-gain adaptive velocity feedback. It is shown that the formulated control is capable of stabilizing exponentially the closed loop system.

中文翻译：

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非线性轴向移动弦的自适应边界稳定

在本文中，我们感兴趣的是通过自适应边界控制来稳定非线性轴向移动的弦。闭环系统解的存在唯一性在非线性半群理论的框架内通过使用 Crandall-Liggett 定理来处理。该控制是通过低增益自适应速度反馈构建的。结果表明，公式化控制能够以指数方式稳定闭环系统。