基于间歇单点测量的PDE系统观测器设计及应用

Observer Design for PDE System Based on Intermittent Pointwise Measurement and Its Application

针对一类由偏微分方程(PDE)表示的非线性时滞分布参数系统的状态估计问题,首先,提出一种新的测量方案——间歇单点测量,并设计了目标系统的状态观测器。间歇单点测量是在单点测量的基础上设计的,将采样环节进一步优化,大大减少了传感器的工作时间,有效节省了通信资源。然后,基于该测量方法设计了一个全维状态观测器,并利用李雅普诺夫理论和积分不等式方法得到了保证估计误差指数收敛,并满足H∞性能指标的有效准则。最后,通过仿真实例验证了所设计观测器的有效性,并将主要结果应用于传染病防治中,成功完成了对易感人群和感染人群时空分布情况的估计,说明了主要结果的实用性。

For the state estimation problem of a class of nonlinear delayed distributed parameter systems represented by partial differential equations(PDE),a novel measurement scheme called intermittent pointwise measurement is proposed,and the state observer of the target system is designed.The intermittent pointwise measurement is designed on the basis of pointwise measurement,which further optimizes the sampling links,greatly reduces the working time of the sensor,and effectively saves the communication resources.Then,a full-dimensional state observer is designed based on this measuring method,and an effective criterion is obtained by using Lyapunov theory and integral inequality methods to guarantee that the estimation error converges exponentially and satisfies the H∞performance index.Finally,the effectiveness of the designed observer is verified by simulation examples,andthe main results are applied to the prevention and treatment of infectious diseases,and the spatiotemporal distribution of the susceptible population and infected population are estimated successfully,which illustrates the practicality of the main results of this paper.