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

中文关键词  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

英文关键词  PDE-ODE cascaded systems  cascade observer  stability  backstepping-like method

中文摘要

      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

英文摘要

      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.