一类一阶双曲型偏微分方程的边界控制

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。

Boundary Control of a First-order Hyperbolic PDE

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.