EXACT CONTROLLABILITY OF AN INTERCONNECTED SYSTEM OF EULER-BERNOULLI BEAM AND WAVE EQUATION THROUGH BOUNDARY COUPLING

Fei Wang; Jun Min Wang; Li Wang

doi:10.3934/eect.2026086

EXACT CONTROLLABILITY OF AN INTERCONNECTED SYSTEM OF EULER-BERNOULLI BEAM AND WAVE EQUATION THROUGH BOUNDARY COUPLING

Fei Wang
, Jun Min Wang^*
, Li Wang

^*Corresponding author for this work

School of Basic Education
Beijing Institute of Graphic Communication
Beijing Institute of Technology
School of Mathematics
Jinzhong University

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we analyze the exact controllability of an Euler-Bernoulli beam through boundary coupling a wave equation, where a boundary control is designed only at the wave equation. By using spectral analysis, we calculate the asymptotic expansion of the eigenvalues and the eigenfunctions for the corresponding dual system and prove the observability inequality holds. Finally, based on the Hilbert Uniqueness Method, we obtain the exact controllability of the original system.

Original language	English
Pages (from-to)	130-144
Number of pages	15
Journal	Evolution Equations and Control Theory
Volume	25
DOIs	https://doi.org/10.3934/eect.2026086
Publication status	Published - 2026
Externally published	Yes

Keywords

Euler-Bernoulli beam
exact controllability
spectral analysis
the Hilbert Uniqueness Method
wave equation

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10.3934/eect.2026086

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title = "EXACT CONTROLLABILITY OF AN INTERCONNECTED SYSTEM OF EULER-BERNOULLI BEAM AND WAVE EQUATION THROUGH BOUNDARY COUPLING",

abstract = "In this paper, we analyze the exact controllability of an Euler-Bernoulli beam through boundary coupling a wave equation, where a boundary control is designed only at the wave equation. By using spectral analysis, we calculate the asymptotic expansion of the eigenvalues and the eigenfunctions for the corresponding dual system and prove the observability inequality holds. Finally, based on the Hilbert Uniqueness Method, we obtain the exact controllability of the original system.",

keywords = "Euler-Bernoulli beam, exact controllability, spectral analysis, the Hilbert Uniqueness Method, wave equation",

author = "Fei Wang and Wang, \{Jun Min\} and Li Wang",

year = "2026",

doi = "10.3934/eect.2026086",

language = "English",

volume = "25",

pages = "130--144",

journal = "Evolution Equations and Control Theory",

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publisher = "American Institute of Mathematical Sciences",

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AU - Wang, Fei

AU - Wang, Jun Min

AU - Wang, Li

PY - 2026

Y1 - 2026

N2 - In this paper, we analyze the exact controllability of an Euler-Bernoulli beam through boundary coupling a wave equation, where a boundary control is designed only at the wave equation. By using spectral analysis, we calculate the asymptotic expansion of the eigenvalues and the eigenfunctions for the corresponding dual system and prove the observability inequality holds. Finally, based on the Hilbert Uniqueness Method, we obtain the exact controllability of the original system.

AB - In this paper, we analyze the exact controllability of an Euler-Bernoulli beam through boundary coupling a wave equation, where a boundary control is designed only at the wave equation. By using spectral analysis, we calculate the asymptotic expansion of the eigenvalues and the eigenfunctions for the corresponding dual system and prove the observability inequality holds. Finally, based on the Hilbert Uniqueness Method, we obtain the exact controllability of the original system.

KW - Euler-Bernoulli beam

KW - exact controllability

KW - spectral analysis

KW - the Hilbert Uniqueness Method

KW - wave equation

UR - https://www.scopus.com/pages/publications/105046110574

U2 - 10.3934/eect.2026086

DO - 10.3934/eect.2026086

M3 - Article

AN - SCOPUS:105046110574

SN - 2163-2472

VL - 25

SP - 130

EP - 144

JO - Evolution Equations and Control Theory

JF - Evolution Equations and Control Theory

ER -

EXACT CONTROLLABILITY OF AN INTERCONNECTED SYSTEM OF EULER-BERNOULLI BEAM AND WAVE EQUATION THROUGH BOUNDARY COUPLING

Abstract

Keywords

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