研究了基于边界输出反馈非线性波方程的自适应控制稳定性问题. 利用可测的终端速度, 获得了高增益自适应控制器, 使用加辽金方法获得闭环系统解的存在性与唯一性, 同时, 证明闭环系统是指数稳定的.

This paper studies adaptive control stability for a nonlinear wave equation under boundary output feedback. A gain adaptive controller is designed in terms of measured end velocity. The existence and uniqueness of the classical solution of the closed-loop system is obtained by using the Galerkin approximation scheme. Meanwhile, the exponential stability of the closed-loop system is obtained.