一类多输入多输出级联系统的边界控制  

On the Boundary Control of a Cascade PDE-ODE in Multi-Input and Multi-Output LTI System

作　　者：甄志远[1] 谢成康[1] 何翠华[1] 

机构地区：[1]西南大学数学与统计学院,重庆400715

出　　处：《西南大学学报（自然科学版）》2016年第5期119-124,共6页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金项目(11301427)

摘　　要：主要研究了两个反应扩散方程和常微分方程的级联控制系统,在更新原有的Backstepping方法基础上,应用常微分上的线性变换,根据相应条件得到核方程,进而得到核方程的解和控制律.通过逆变换及Lypunov证明闭环系统是指数稳定的.In this paper, the boundary control of a cascade control system is considered, which reflects the reaction-diffusion equation and an ordinary differential equation. The ODE of linear transformation is ap- plied in the updating of the original backstepping transformation method. The kernel functions are obtained based on the corresponding conditions, then the kernel solutions and the control law are obtained. The closed loop system is exponentially stable by proving inverse transformation and Lyapunov function.

关 键 词：级联系统 闭环系统 边界控制 稳定性 

分 类 号：O231.2[理学—运筹学与控制论]