A backstepping approach to adaptive error feedback regulator design for one-dimensional linear parabolic PIDEs

Wei Wei Liu; Jun Min Wang; Wei Guo

doi:10.1016/j.jmaa.2021.125310

A backstepping approach to adaptive error feedback regulator design for one-dimensional linear parabolic PIDEs

Wei Wei Liu, Jun Min Wang, Wei Guo^*

^*Corresponding author for this work

School of Mathematics and Statistics

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

9 Citations (Scopus)

Abstract

This paper considers the error feedback regulator problem (EFRP) of one-dimensional parabolic partial integro-differential equations (PIDEs) in which the boundary disturbance and the tracking error are both anti-collocated with the control. Firstly, we construct the first auxiliary control system where the output is the measured tracking error. Then the observer and estimators are designed in terms of the measured error to recover the state of the auxiliary control system and estimate the unknown parameters. Secondly, we construct the second auxiliary control system in which the disturbance becomes collocated with the control. Finally, the regulator is proposed based on the backstepping method presented in [33] to make the state of the closed-loop system bounded and the tracking error asymptotically convergent to zero.

Original language	English
Article number	125310
Journal	Journal of Mathematical Analysis and Applications
Volume	503
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2021.125310
Publication status	Published - 15 Nov 2021

Keywords

Adaptive control
Backstepping method
Output regulation
Parabolic PIDE

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10.1016/j.jmaa.2021.125310

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title = "A backstepping approach to adaptive error feedback regulator design for one-dimensional linear parabolic PIDEs",

abstract = "This paper considers the error feedback regulator problem (EFRP) of one-dimensional parabolic partial integro-differential equations (PIDEs) in which the boundary disturbance and the tracking error are both anti-collocated with the control. Firstly, we construct the first auxiliary control system where the output is the measured tracking error. Then the observer and estimators are designed in terms of the measured error to recover the state of the auxiliary control system and estimate the unknown parameters. Secondly, we construct the second auxiliary control system in which the disturbance becomes collocated with the control. Finally, the regulator is proposed based on the backstepping method presented in [33] to make the state of the closed-loop system bounded and the tracking error asymptotically convergent to zero.",

keywords = "Adaptive control, Backstepping method, Output regulation, Parabolic PIDE",

author = "Liu, {Wei Wei} and Wang, {Jun Min} and Wei Guo",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",

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AU - Liu, Wei Wei

AU - Wang, Jun Min

AU - Guo, Wei

PY - 2021/11/15

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N2 - This paper considers the error feedback regulator problem (EFRP) of one-dimensional parabolic partial integro-differential equations (PIDEs) in which the boundary disturbance and the tracking error are both anti-collocated with the control. Firstly, we construct the first auxiliary control system where the output is the measured tracking error. Then the observer and estimators are designed in terms of the measured error to recover the state of the auxiliary control system and estimate the unknown parameters. Secondly, we construct the second auxiliary control system in which the disturbance becomes collocated with the control. Finally, the regulator is proposed based on the backstepping method presented in [33] to make the state of the closed-loop system bounded and the tracking error asymptotically convergent to zero.

AB - This paper considers the error feedback regulator problem (EFRP) of one-dimensional parabolic partial integro-differential equations (PIDEs) in which the boundary disturbance and the tracking error are both anti-collocated with the control. Firstly, we construct the first auxiliary control system where the output is the measured tracking error. Then the observer and estimators are designed in terms of the measured error to recover the state of the auxiliary control system and estimate the unknown parameters. Secondly, we construct the second auxiliary control system in which the disturbance becomes collocated with the control. Finally, the regulator is proposed based on the backstepping method presented in [33] to make the state of the closed-loop system bounded and the tracking error asymptotically convergent to zero.

KW - Adaptive control

KW - Backstepping method

KW - Output regulation

KW - Parabolic PIDE

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DO - 10.1016/j.jmaa.2021.125310

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AN - SCOPUS:85106253577

SN - 0022-247X

VL - 503

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

M1 - 125310

ER -

A backstepping approach to adaptive error feedback regulator design for one-dimensional linear parabolic PIDEs

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