Adaptive stabilization for a wave equation subject to boundary control matched harmonic disturbance

IF 1.6 4区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

IMA Journal of Mathematical Control and Information Pub Date : 2023-05-14 DOI:10.1093/imamci/dnad010

Jun-Jun Liu, Yanxiao Zhao

引用次数: 0

Abstract

In this paper, we are concerned with adaptive stabilization for a wave equation subject to boundary control matched harmonic disturbance. We use the adaptive and Lyapunov approach to estimate unknown disturbance and construct an adaptive boundary feedback controller. By the semigroup theory and Lasalle‘s invariance theorem, the well-posedness and asymptotic stability of the closed-loop system is proved, respectively. At the same time, it is shown that the parameter estimates involved in the constructed controller converge to their own real values as time goes to infinity. Some numerical simulations are offered at the end of the paper to illustrate the effectiveness of theoretical results.

查看原文本刊更多论文

边界控制下匹配谐波扰动波动方程的自适应镇定

本文研究了边界控制匹配谐波扰动下波动方程的自适应镇定问题。我们使用自适应和李雅普诺夫方法来估计未知扰动，并构造了一个自适应边界反馈控制器。利用半群理论和Lasalle不变性定理，分别证明了闭环系统的适定性和渐近稳定性。同时，随着时间的推移，所构造的控制器中涉及的参数估计收敛到它们自己的实值。文末给出了一些数值模拟，以说明理论结果的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

IMA Journal of Mathematical Control and Information 工程技术-应用数学

CiteScore

3.30

自引率

6.70%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal is to provide an outlet for papers which are original and of high quality in mathematical control theory, systems theory, and applied information sciences. Short papers and mathematical correspondence or technical notes will be welcome, although the primary function of the journal is to publish papers of substantial length and coverage. The emphasis will be upon relevance, originality and clarify of presentation, although timeliness may well be an important feature in acceptable papers. Speculative papers that suggest new avenues for research or potential solutions to unsolved problems of control and information theory will be particularly welcome. Specific application papers will not normally be within the remit of the journal. Applications that illustrate techniques or theories will be acceptable. A prime function of the journal is to encourage the interplay between control and information theory and other mathematical sciences. All submitted papers will be judged on their merits by at least two referees and a full paper report will be available to the intending authors. Submitted articles will in general be published in an issue within six months of submission. Papers should not have previously published, nor should they be undes consideration for publication in another journal. This Journal takes publication ethics very seriously. If misconduct is found or suspected after the manuscript is published, the journal will investigate the matter and this may result in the article subsequently being retracted.