Dynamic control for one-dimensional wave equation with nonlinear boundary

Xiao Hui Wu; Jun Min Wang; Fei Wang

doi:10.1016/j.jmaa.2026.131047

Dynamic control for one-dimensional wave equation with nonlinear boundary

Xiao Hui Wu
, Jun Min Wang^*
, Fei Wang

^*Corresponding author for this work

The School of Statistics and Mathematics
Shanxi University
Beijing Institute of Technology
School of Basic Education
Beijing Institute of Graphic Communication

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

Abstract

In this paper, we investigate the output feedback stabilization of wave equation with Van Der Pol type boundary condition and disturbance. By expanding interactive integral control, we propose a novel method to compensate for disturbance by using non-collocated boundary measurements. Based on this method, we design two types of dynamic feedback control laws to stabilize the system. Afterwards, the numerical experiments are carried out to illustrate the proposed approach.

Original language	English
Article number	131047
Journal	Journal of Mathematical Analysis and Applications
Volume	566
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2026.131047
Publication status	Published - 1 Feb 2027
Externally published	Yes

Keywords

Disturbance rejection
Non-collocated measurements
Nonlinear boundary
Stabilization
Wave equation

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10.1016/j.jmaa.2026.131047

Cite this

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title = "Dynamic control for one-dimensional wave equation with nonlinear boundary",

abstract = "In this paper, we investigate the output feedback stabilization of wave equation with Van Der Pol type boundary condition and disturbance. By expanding interactive integral control, we propose a novel method to compensate for disturbance by using non-collocated boundary measurements. Based on this method, we design two types of dynamic feedback control laws to stabilize the system. Afterwards, the numerical experiments are carried out to illustrate the proposed approach.",

keywords = "Disturbance rejection, Non-collocated measurements, Nonlinear boundary, Stabilization, Wave equation",

author = "Wu, \{Xiao Hui\} and Wang, \{Jun Min\} and Fei Wang",

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AU - Wang, Jun Min

AU - Wang, Fei

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N2 - In this paper, we investigate the output feedback stabilization of wave equation with Van Der Pol type boundary condition and disturbance. By expanding interactive integral control, we propose a novel method to compensate for disturbance by using non-collocated boundary measurements. Based on this method, we design two types of dynamic feedback control laws to stabilize the system. Afterwards, the numerical experiments are carried out to illustrate the proposed approach.

AB - In this paper, we investigate the output feedback stabilization of wave equation with Van Der Pol type boundary condition and disturbance. By expanding interactive integral control, we propose a novel method to compensate for disturbance by using non-collocated boundary measurements. Based on this method, we design two types of dynamic feedback control laws to stabilize the system. Afterwards, the numerical experiments are carried out to illustrate the proposed approach.

KW - Disturbance rejection

KW - Non-collocated measurements

KW - Nonlinear boundary

KW - Stabilization

KW - Wave equation

UR - https://www.scopus.com/pages/publications/105048944270

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JO - Journal of Mathematical Analysis and Applications

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ER -

Dynamic control for one-dimensional wave equation with nonlinear boundary

Abstract

Keywords

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