Stabilization of Series Heat Equations with One Boundary Control

Lina Pan; Jun Min Wang

doi:10.1007/s10883-022-09618-w

Stabilization of Series Heat Equations with One Boundary Control

Lina Pan^*, Jun Min Wang

^*Corresponding author for this work

School of Mathematics and Statistics

Beijing Institute of Technology

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

2 Citations (Scopus)

Abstract

In this paper, we consider the exponential stabilization for a series system of N heat equations, where one boundary control is only applied to the leading (first) heat equation, and the boundary temperature of the previous heat is fed into the boundary heat flux of the next one. With N invertible transformations, we present a boundary feedback control so that the closed-loop system is equivalent to an exponentially stable target system. Some numerical simulation results are presented to validate the theoretical conclusions.

Original language	English
Pages (from-to)	969-987
Number of pages	19
Journal	Journal of Dynamical and Control Systems
Volume	29
Issue number	3
DOIs	https://doi.org/10.1007/s10883-022-09618-w
Publication status	Published - Sept 2023

Keywords

35A01
65L10
65L12
65L20
65L70
N heat equations
Series system
Stabilization

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10.1007/s10883-022-09618-w

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Pan, L., & Wang, J. M. (2023). Stabilization of Series Heat Equations with One Boundary Control. Journal of Dynamical and Control Systems, 29(3), 969-987. https://doi.org/10.1007/s10883-022-09618-w

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abstract = "In this paper, we consider the exponential stabilization for a series system of N heat equations, where one boundary control is only applied to the leading (first) heat equation, and the boundary temperature of the previous heat is fed into the boundary heat flux of the next one. With N invertible transformations, we present a boundary feedback control so that the closed-loop system is equivalent to an exponentially stable target system. Some numerical simulation results are presented to validate the theoretical conclusions.",

keywords = "35A01, 65L10, 65L12, 65L20, 65L70, N heat equations, Series system, Stabilization",

author = "Lina Pan and Wang, {Jun Min}",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

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T1 - Stabilization of Series Heat Equations with One Boundary Control

AU - Pan, Lina

AU - Wang, Jun Min

PY - 2023/9

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AB - In this paper, we consider the exponential stabilization for a series system of N heat equations, where one boundary control is only applied to the leading (first) heat equation, and the boundary temperature of the previous heat is fed into the boundary heat flux of the next one. With N invertible transformations, we present a boundary feedback control so that the closed-loop system is equivalent to an exponentially stable target system. Some numerical simulation results are presented to validate the theoretical conclusions.

KW - 35A01

KW - 65L10

KW - 65L12

KW - 65L20

KW - 65L70

KW - N heat equations

KW - Series system

KW - Stabilization

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EP - 987

JO - Journal of Dynamical and Control Systems

JF - Journal of Dynamical and Control Systems

IS - 3

ER -

Stabilization of Series Heat Equations with One Boundary Control

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Keywords

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