Error-based output tracking for a one-dimensional wave equation with harmonic type disturbance

被引：0

作者：

Tian Z. ^{[1
]}

Wu X.-H. ^{[2
]}

机构：

[1] Department of Economics, University of Michigan, Ann Arbor, 48104, MI

[2] School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi

来源：

IMA Journal of Mathematical Control and Information | 2021年 / 37卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Disturbance; Observer; Output tracking; Stabilization; Wave equation;

D O I：

10.1093/IMAMCI/DNAA020

中图分类号：

学科分类号：

摘要：

In this paper, we consider output tracking for a one-dimensional wave equation, where the boundary disturbances are either collocated or non-collocated with control. The regulated output and the control are supposed to be non-collocated with control, which represents a difficult case for output tracking of PDEs. We apply the trajectory planning approach to design an observer, in terms of tracking error only, to estimate both states of the system and the exosystem from which the disturbances are produced. An error-based feedback control is proposed by solving a standard regulator equation. It is shown that (a) the closed-loop system is uniformly bounded whenever the exosystem is bounded; (b) when the disturbance is zero, the closed-loop is asymptotically stable; and (c) the tracking error converges to zero asymptotically as time goes to infinity. Numerical simulations are performed to validate the effectiveness of the proposed control. © The Author(s) 2020. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

引用

页码：1447 / 1467

页数：20

共 22 条

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