星形明渠网络系统的PDP反馈控制和指数镇定  

The PDP Feedback Control and Exponential Stabilization of a Star-Shaped Open Channels Network System

作　　者：庞玉婷 赵东霞 Pang Yuting;Zhao Dongxia(School of Science,North University of China,Taiyuan 030051)

机构地区：[1]中北大学数学学院,太原030051

出　　处：《数学物理学报（A辑）》2023年第6期1803-1813,共11页Acta Mathematica Scientia

基　　金：山西省基础研究计划资助项目(20210302123046)。

摘　　要：该文研究基于Saint-Venant方程组的具有底部坡度和底部摩擦的星形明渠网络,该系统包含n个子系统:n-1个入口通道和1个出口通道.设在线输出量测和输入控制均位于边界上,结合闸门前后流量关系等约束,建立了具有瞬时位置和时滞位置线性组合的反馈控制律.考虑到时滞项可由一阶双曲偏微分方程刻画,并结合黎曼坐标变换和线性化手段将闭环系统改写为PDE-PDE无穷维耦合系统的形式.通过构造加权Lyapunov函数讨论了系统在L2范数下的指数稳定性,给出了控制参数和时滞值的充分条件,进而证明了在线输出量测被调控到指定的参考信号.最后,利用Matlab数学软件进行数值仿真,佐证参数条件的合理性和结论的有效性.Based on the Saint-Venant equations,the star-shaped open channel network with bottom slope and bottom friction is studied in this paper.The system consists of n subsystems:n-1 inlet channels and one outlet channel.It is assumed that both online output measurement and input control are located on the boundary.The feedback control law with a linear combination of position and delayed position is established based on the restriction of flow relation before and after the gate.Considering that the delay term can be characterized by the first-order hyperbolic partial differential equation,the closed-loop system is rewritten into the form of PDE-PDE infinite-dimensional coupling system by means of Riemannian coordinate transformation and linearization.By constructing the weighted Lyapunov function,the exponential stability of the system under the L~2-norm is discussed,and the sufficient conditions for the control parameters and time-delay value are given.Furthermore,it is proved that the online output measurement is regulated to the specified reference signal.Finally,numerical simulation is carried out by using Matlab to prove the rationality of the parameters conditions and the validity of the conclusion.

关 键 词：Saint-Venant方程组 PDP反馈控制器 LYAPUNOV方法 指数稳定性 

分 类 号：O231.4[理学—运筹学与控制论]