Input-to-State Stabilization for an ODE Cascaded by a Parabolic PIDE with Disturbances

Hanwen Zhang; Junmin Wang; Jianjun Gu

doi:10.1109/CCDC52312.2021.9602220

Input-to-State Stabilization for an ODE Cascaded by a Parabolic PIDE with Disturbances

Hanwen Zhang, Junmin Wang, Jianjun Gu

School of Mathematics and Statistics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

This paper investigates the input-to-state stabilization problem of an ODE cascaded by a parabolic partial integro-differential equation (PIDE) subject to disturbances. First, the backstepping approach and the sliding mode control method are used to design the discontinuous boundary feedback control law. Then, a Galerkin approximation scheme is constructed to show the existence of solution to the closed-loop system. With the Lyapunov approach, the input-to-state stability of the closed-loop system is obtained. Finally, the simulation results are presented to illustrate the effectiveness of the proposed control law.

Original language	English
Title of host publication	Proceedings of the 33rd Chinese Control and Decision Conference, CCDC 2021
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	979-984
Number of pages	6
ISBN (Electronic)	9781665440899
DOIs	https://doi.org/10.1109/CCDC52312.2021.9602220
Publication status	Published - 2021
Event	33rd Chinese Control and Decision Conference, CCDC 2021 - Kunming, China Duration: 22 May 2021 → 24 May 2021

Publication series

Name	Proceedings of the 33rd Chinese Control and Decision Conference, CCDC 2021

Conference

Conference	33rd Chinese Control and Decision Conference, CCDC 2021
Country/Territory	China
City	Kunming
Period	22/05/21 → 24/05/21

Keywords

Disturbance rejection
Input-to-state stabilization
Parabolic partial integro-differential equation
Sliding mode control method

Access to Document

10.1109/CCDC52312.2021.9602220

Cite this

Zhang, H., Wang, J., & Gu, J. (2021). Input-to-State Stabilization for an ODE Cascaded by a Parabolic PIDE with Disturbances. In Proceedings of the 33rd Chinese Control and Decision Conference, CCDC 2021 (pp. 979-984). (Proceedings of the 33rd Chinese Control and Decision Conference, CCDC 2021). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CCDC52312.2021.9602220

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title = "Input-to-State Stabilization for an ODE Cascaded by a Parabolic PIDE with Disturbances",

abstract = "This paper investigates the input-to-state stabilization problem of an ODE cascaded by a parabolic partial integro-differential equation (PIDE) subject to disturbances. First, the backstepping approach and the sliding mode control method are used to design the discontinuous boundary feedback control law. Then, a Galerkin approximation scheme is constructed to show the existence of solution to the closed-loop system. With the Lyapunov approach, the input-to-state stability of the closed-loop system is obtained. Finally, the simulation results are presented to illustrate the effectiveness of the proposed control law.",

keywords = "Disturbance rejection, Input-to-state stabilization, Parabolic partial integro-differential equation, Sliding mode control method",

author = "Hanwen Zhang and Junmin Wang and Jianjun Gu",

note = "Publisher Copyright: {\textcopyright} 2021 IEEE.; 33rd Chinese Control and Decision Conference, CCDC 2021 ; Conference date: 22-05-2021 Through 24-05-2021",

year = "2021",

doi = "10.1109/CCDC52312.2021.9602220",

language = "English",

series = "Proceedings of the 33rd Chinese Control and Decision Conference, CCDC 2021",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "979--984",

booktitle = "Proceedings of the 33rd Chinese Control and Decision Conference, CCDC 2021",

address = "United States",

}

Zhang, H, Wang, J & Gu, J 2021, Input-to-State Stabilization for an ODE Cascaded by a Parabolic PIDE with Disturbances. in Proceedings of the 33rd Chinese Control and Decision Conference, CCDC 2021. Proceedings of the 33rd Chinese Control and Decision Conference, CCDC 2021, Institute of Electrical and Electronics Engineers Inc., pp. 979-984, 33rd Chinese Control and Decision Conference, CCDC 2021, Kunming, China, 22/05/21. https://doi.org/10.1109/CCDC52312.2021.9602220

Input-to-State Stabilization for an ODE Cascaded by a Parabolic PIDE with Disturbances. / Zhang, Hanwen; Wang, Junmin; Gu, Jianjun.
Proceedings of the 33rd Chinese Control and Decision Conference, CCDC 2021. Institute of Electrical and Electronics Engineers Inc., 2021. p. 979-984 (Proceedings of the 33rd Chinese Control and Decision Conference, CCDC 2021).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Input-to-State Stabilization for an ODE Cascaded by a Parabolic PIDE with Disturbances

AU - Zhang, Hanwen

AU - Wang, Junmin

AU - Gu, Jianjun

PY - 2021

Y1 - 2021

N2 - This paper investigates the input-to-state stabilization problem of an ODE cascaded by a parabolic partial integro-differential equation (PIDE) subject to disturbances. First, the backstepping approach and the sliding mode control method are used to design the discontinuous boundary feedback control law. Then, a Galerkin approximation scheme is constructed to show the existence of solution to the closed-loop system. With the Lyapunov approach, the input-to-state stability of the closed-loop system is obtained. Finally, the simulation results are presented to illustrate the effectiveness of the proposed control law.

AB - This paper investigates the input-to-state stabilization problem of an ODE cascaded by a parabolic partial integro-differential equation (PIDE) subject to disturbances. First, the backstepping approach and the sliding mode control method are used to design the discontinuous boundary feedback control law. Then, a Galerkin approximation scheme is constructed to show the existence of solution to the closed-loop system. With the Lyapunov approach, the input-to-state stability of the closed-loop system is obtained. Finally, the simulation results are presented to illustrate the effectiveness of the proposed control law.

KW - Disturbance rejection

KW - Input-to-state stabilization

KW - Parabolic partial integro-differential equation

KW - Sliding mode control method

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U2 - 10.1109/CCDC52312.2021.9602220

DO - 10.1109/CCDC52312.2021.9602220

M3 - Conference contribution

AN - SCOPUS:85125195921

T3 - Proceedings of the 33rd Chinese Control and Decision Conference, CCDC 2021

SP - 979

EP - 984

BT - Proceedings of the 33rd Chinese Control and Decision Conference, CCDC 2021

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 33rd Chinese Control and Decision Conference, CCDC 2021

Y2 - 22 May 2021 through 24 May 2021

ER -

Zhang H, Wang J, Gu J. Input-to-State Stabilization for an ODE Cascaded by a Parabolic PIDE with Disturbances. In Proceedings of the 33rd Chinese Control and Decision Conference, CCDC 2021. Institute of Electrical and Electronics Engineers Inc. 2021. p. 979-984. (Proceedings of the 33rd Chinese Control and Decision Conference, CCDC 2021). doi: 10.1109/CCDC52312.2021.9602220

Input-to-State Stabilization for an ODE Cascaded by a Parabolic PIDE with Disturbances

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