Output-feedback stabilization of an underactuated network of N interconnected n + m hyperbolic PDE systems

Jean AuriolL2S
{"title":"Output-feedback stabilization of an underactuated network of N interconnected n + m hyperbolic PDE systems","authors":"Jean AuriolL2S","doi":"arxiv-2409.10087","DOIUrl":null,"url":null,"abstract":"In this article, we detail the design of an output feedback stabilizing\ncontrol law for an underactuated network of N subsystems of n + m\nheterodirectional linear first-order hyperbolic Partial Differential Equations\ninterconnected through their boundaries. The network has a chain structure, as\nonly one of the subsystems is actuated. The available measurements are located\nat the opposite extremity of the chain. The proposed approach introduces a new\ntype of integral transformation to tackle in-domain couplings in the different\nsubsystems while guaranteeing a ''clear actuation path'' between the control\ninput and the different subsystems. Then, it is possible to state several\nessential properties of each subsystem: output trajectory tracking,\ninput-to-state stability, and predictability (the possibility of designing a\nstate prediction). We recursively design a stabilizing state-feedback\ncontroller by combining these properties. We then design a state-observer that\nreconstructs delayed values of the states. This observer is combined with the\nstate-feedback control law to obtain an output-feedback controller. Simulations\ncomplete the presentation.","PeriodicalId":501165,"journal":{"name":"arXiv - MATH - Analysis of PDEs","volume":"29 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Analysis of PDEs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10087","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

Abstract

In this article, we detail the design of an output feedback stabilizing control law for an underactuated network of N subsystems of n + m heterodirectional linear first-order hyperbolic Partial Differential Equations interconnected through their boundaries. The network has a chain structure, as only one of the subsystems is actuated. The available measurements are located at the opposite extremity of the chain. The proposed approach introduces a new type of integral transformation to tackle in-domain couplings in the different subsystems while guaranteeing a ''clear actuation path'' between the control input and the different subsystems. Then, it is possible to state several essential properties of each subsystem: output trajectory tracking, input-to-state stability, and predictability (the possibility of designing a state prediction). We recursively design a stabilizing state-feedback controller by combining these properties. We then design a state-observer that reconstructs delayed values of the states. This observer is combined with the state-feedback control law to obtain an output-feedback controller. Simulations complete the presentation.
由 N 个相互连接的 n + m 个双曲 PDE 系统组成的欠激励网络的输出反馈稳定问题
在本文中,我们详细介绍了如何为一个由 n + m 个双向线性一阶双曲偏微分方程的 N 个子系统组成的欠驱动网络设计输出反馈稳定控制法。该网络具有链式结构,因为只有一个子系统被驱动。可用的测量值位于链的两端。所提出的方法引入了一种新型积分变换,以解决不同子系统中的域内耦合问题,同时保证控制输入和不同子系统之间有 "清晰的执行路径"。然后,就有可能说明每个子系统的几个基本特性:输出轨迹跟踪、输入到状态的稳定性和可预测性(设计状态预测的可能性)。我们结合这些特性,递归设计出一个稳定的状态反馈控制器。然后,我们设计一个状态观测器,用于重建状态的延迟值。该观测器与状态反馈控制法相结合,就得到了输出反馈控制器。模拟完成演示。
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
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信