一类一阶双曲型偏微分方程的边界控制

摘要

This paper considers stabilization of a first-order hyperbolic PDE by using backstepping method of boundary control. For designing the controller, a modificative backstepping transformation is introduced. Through a series of mathematical computation, the exact solutions of kernels are obtained, and a control law is obtained specifically. Finally, for obtaining stabilization of the closed-loop system, the inverse imformation is found.%本文研究了一类一阶双曲型偏微分方程的边界控制问题，利用边界控制的反推法设计出反馈控制器。在设计控制器的过程中，改进了反推法中常用的积分变换，同时经过一系列数学计算解出积分变换中的核函数，从而设计出闭环系统的反馈控制器，最后，为了得到闭环系统的稳定性，找到积分变换的逆变换。