Boundary stabilization of linear hyperbolic integro-differential equation with time-dependent coefficients

IF 5.9 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica Pub Date : 2025-06-17 DOI:10.1016/j.automatica.2025.112451

Long Hu , Qing Zhang

引用次数: 0

Abstract

This paper is concerned with the boundary stabilization in finite time of first-order linear hyperbolic partial integro-differential equation (PIDE) with time-varying coefficients. By extending the so-called backstepping method, we derive a full-state feedback control law that allows the closed-loop system to converge to the zero equilibrium under minimal settling time. The well-posedness of the kernel equation, which evolves on the multi-dimensional unbounded spatiotemporal domain, is the main technical problem, the proof of which requires careful use of successive approximation approach with new recursive bound. This work extends existing results for the system where the characteristic speed was only time-independent.

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具有时变系数的线性双曲型积分-微分方程的边界稳定

研究一类一阶时变系数线性双曲型偏积分-微分方程在有限时间内的边界镇定问题。通过对退步法的扩展，我们得到了一种允许闭环系统在最小的沉降时间下收敛到零平衡点的全状态反馈控制律。核方程在多维无界时空域中演化，核方程的适定性是主要的技术问题，其证明需要谨慎地使用具有新递推界的逐次逼近方法。这项工作扩展了已有的系统结果，其中特征速度仅与时间无关。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Automatica 工程技术-工程：电子与电气

CiteScore

10.70

自引率

7.80%

发文量

617

审稿时长

5 months

期刊介绍： Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field. After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience. Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.