带有大输出时滞的ODE–热方程级联系统的观测器设计  

Observer design for a cascaded ODE-Heat system with a large output delay

作　　者：张静 康文 ZHANG Jing;KANG Wen(School of Automation and Electrical Engineering,University of Science and Technology Beijing,Beijing 100083,China;School of Mathematics and Statistics,Beijing Institute of Technology,Beijing 100081,China;Key Laboratory of Mathematical Theory and Computation in Information Security,Beijing Institute of Technology,Beijing 102488,China)

机构地区：[1]北京科技大学自动化学院,北京100083 [2]北京理工大学数学与统计学院,北京100081 [3]北京理工大学信息安全的数学理论与计算机工业和信息化部重点实验室,北京102488

出　　处：《控制理论与应用》2023年第8期1417-1425,共9页Control Theory & Applications

基　　金：国家自然科学基金面上项目(62273046);广东省基础与应用基础研究基金面上项目(2022A1515010039);北京理工大学青年教师学术启动计划项目(3170012222207)资助。

摘　　要：为了估计系统的状态并补偿输出时滞,本文提出一种新颖的观测器设计方法应用在常微分方程(ODE)-热方程级联系统中.不同于传统观测器的设计方法,该方法的核心思想是将大时滞划分为若干段小时滞,再设计一串级联的子观测器逐步地估计系统的状态.这种方法的优势在于对于大时滞仍有效.本文通过backstepping-like方法实现了原系统与目标系统的等价变换,结合Lyapunov-Krasovskii方法和线性矩阵不等式理论,得到了误差系统指数稳定的结果.最后,通过仿真实例验证了级联观测器的有效性.This paper provides a novel observer design for a cascaded ordinary differential equation(ODE)-heat system to estimate the state of the system and compensate the output delay.Different from the traditional observer schemes,the core idea of this method is to divide the large delay into small pieces and a chain of cascaded sub-observers is designed to achieve the state estimation sequentially.The advantage of this approach is that the large delay can be compensated.For stability analysis,the backstepping-like method is employed to transform the original system into an equivalent target system.By the Lyapunov-Krasovskii method and the linear matrix inequality theory,the exponential stability analysis of the error system is established.Finally,a numerical simulation is presented to demonstrate the effectiveness of the proposed method.

关 键 词：偏微分方程与常微分方程(PDE-ODE)级联系统 级联观测器 稳定性 backstepping-like方法 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]