{"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.
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。