Adaptive output tracking for 1-D unstable heat equations with unknown multi-frequency exosystem

Jun Chen; Junmin Wang; Xiufang Yu

doi:10.1016/j.cnsns.2025.109142

Adaptive output tracking for 1-D unstable heat equations with unknown multi-frequency exosystem

Jun Chen^*
, Junmin Wang
, Xiufang Yu

^*此作品的通讯作者

Beijing Institute of Technology
Taiyuan University of Technology

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

In this paper, we address the adaptive output tracking problem for a 1-D unstable heat equation with non-collocated configurations. The system is subject to disturbances and reference signals generated by a finite-dimensional exosystem, which possess multiple unknown frequencies and amplitudes. By constructing an auxiliary system and internal model dynamics, we restructure the measurable tracking error composed of available states. An adaptive method is proposed to estimate the uncertain parameters. We design an error-based adaptive dynamic compensator to achieve exponential output tracking using the backstepping method. A numerical example is provided to illustrate the effectiveness of the proposed strategy.

源语言	英语
文章编号	109142
期刊	Communications in Nonlinear Science and Numerical Simulation
卷	152
DOI	https://doi.org/10.1016/j.cnsns.2025.109142
出版状态	已出版 - 1月 2026
已对外发布	是

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title = "Adaptive output tracking for 1-D unstable heat equations with unknown multi-frequency exosystem",

abstract = "In this paper, we address the adaptive output tracking problem for a 1-D unstable heat equation with non-collocated configurations. The system is subject to disturbances and reference signals generated by a finite-dimensional exosystem, which possess multiple unknown frequencies and amplitudes. By constructing an auxiliary system and internal model dynamics, we restructure the measurable tracking error composed of available states. An adaptive method is proposed to estimate the uncertain parameters. We design an error-based adaptive dynamic compensator to achieve exponential output tracking using the backstepping method. A numerical example is provided to illustrate the effectiveness of the proposed strategy.",

keywords = "Adaptive control, Exponential stability, Heat equation, Output tracking, Unknown harmonic signals",

author = "Jun Chen and Junmin Wang and Xiufang Yu",

note = "Publisher Copyright: {\textcopyright} 2025 Elsevier B.V.",

year = "2026",

month = jan,

doi = "10.1016/j.cnsns.2025.109142",

language = "English",

volume = "152",

journal = "Communications in Nonlinear Science and Numerical Simulation",

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T1 - Adaptive output tracking for 1-D unstable heat equations with unknown multi-frequency exosystem

AU - Chen, Jun

AU - Wang, Junmin

AU - Yu, Xiufang

PY - 2026/1

Y1 - 2026/1

N2 - In this paper, we address the adaptive output tracking problem for a 1-D unstable heat equation with non-collocated configurations. The system is subject to disturbances and reference signals generated by a finite-dimensional exosystem, which possess multiple unknown frequencies and amplitudes. By constructing an auxiliary system and internal model dynamics, we restructure the measurable tracking error composed of available states. An adaptive method is proposed to estimate the uncertain parameters. We design an error-based adaptive dynamic compensator to achieve exponential output tracking using the backstepping method. A numerical example is provided to illustrate the effectiveness of the proposed strategy.

AB - In this paper, we address the adaptive output tracking problem for a 1-D unstable heat equation with non-collocated configurations. The system is subject to disturbances and reference signals generated by a finite-dimensional exosystem, which possess multiple unknown frequencies and amplitudes. By constructing an auxiliary system and internal model dynamics, we restructure the measurable tracking error composed of available states. An adaptive method is proposed to estimate the uncertain parameters. We design an error-based adaptive dynamic compensator to achieve exponential output tracking using the backstepping method. A numerical example is provided to illustrate the effectiveness of the proposed strategy.

KW - Adaptive control

KW - Exponential stability

KW - Heat equation

KW - Output tracking

KW - Unknown harmonic signals

UR - https://www.scopus.com/pages/publications/105011061764

U2 - 10.1016/j.cnsns.2025.109142

DO - 10.1016/j.cnsns.2025.109142

M3 - Article

AN - SCOPUS:105011061764

SN - 1007-5704

VL - 152

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

M1 - 109142

ER -

Adaptive output tracking for 1-D unstable heat equations with unknown multi-frequency exosystem

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