Stabilization of a cascade system of ODE-PDE subject to boundary control matched disturbance

Jun Min Wang; Li Li Wang; Jun Jun Liu; Beibei Ren

doi:10.1109/WCICA.2014.7052828

Stabilization of a cascade system of ODE-PDE subject to boundary control matched disturbance

Jun Min Wang, Li Li Wang, Jun Jun Liu, Beibei Ren

Mechanical Engineering

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

Abstract

In this paper, we are concerned with the boundary feedback stabilization of a cascade system of ODE-PDE with the external disturbance flowing the control end, where the PDE is described by a heat equation with Dirichlet interconnection. We use the sliding mode control (SMC) to deal with the disturbance. By the SMC approach, the disturbance is supposed to be bounded only. The existence and uniqueness of the solution for the closed-loop via SMC are proved, and the monotonicity of the 'reaching condition' is presented without the differentiation of the sliding mode function, for which it may not always exist for the weak solution of the closed-loop system.

Original language	English
Title of host publication	Proceeding of the 11th World Congress on Intelligent Control and Automation, WCICA 2014
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	856-860
Number of pages	5
Edition	March
ISBN (Electronic)	9781479958252
DOIs	https://doi.org/10.1109/WCICA.2014.7052828
State	Published - Mar 2 2015
Event	2014 11th World Congress on Intelligent Control and Automation, WCICA 2014 - Shenyang, China Duration: Jun 29 2014 → Jul 4 2014

Publication series

Name	Proceedings of the World Congress on Intelligent Control and Automation (WCICA)
Number	March
Volume	2015-March

Conference

Conference	2014 11th World Congress on Intelligent Control and Automation, WCICA 2014
Country/Territory	China
City	Shenyang
Period	06/29/14 → 07/4/14

Keywords

Backstepping
Boundary control
Cascade systems
Disturbance rejection
Sliding mode control

Access to Document

10.1109/WCICA.2014.7052828

Cite this

Wang, J. M., Wang, L. L., Liu, J. J., & Ren, B. (2015). Stabilization of a cascade system of ODE-PDE subject to boundary control matched disturbance. In Proceeding of the 11th World Congress on Intelligent Control and Automation, WCICA 2014 (March ed., pp. 856-860). Article 7052828 (Proceedings of the World Congress on Intelligent Control and Automation (WCICA); Vol. 2015-March, No. March). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/WCICA.2014.7052828

Wang, Jun Min ; Wang, Li Li ; Liu, Jun Jun et al. / Stabilization of a cascade system of ODE-PDE subject to boundary control matched disturbance. Proceeding of the 11th World Congress on Intelligent Control and Automation, WCICA 2014. March. ed. Institute of Electrical and Electronics Engineers Inc., 2015. pp. 856-860 (Proceedings of the World Congress on Intelligent Control and Automation (WCICA); March).

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title = "Stabilization of a cascade system of ODE-PDE subject to boundary control matched disturbance",

abstract = "In this paper, we are concerned with the boundary feedback stabilization of a cascade system of ODE-PDE with the external disturbance flowing the control end, where the PDE is described by a heat equation with Dirichlet interconnection. We use the sliding mode control (SMC) to deal with the disturbance. By the SMC approach, the disturbance is supposed to be bounded only. The existence and uniqueness of the solution for the closed-loop via SMC are proved, and the monotonicity of the 'reaching condition' is presented without the differentiation of the sliding mode function, for which it may not always exist for the weak solution of the closed-loop system.",

keywords = "Backstepping, Boundary control, Cascade systems, Disturbance rejection, Sliding mode control",

author = "Wang, {Jun Min} and Wang, {Li Li} and Liu, {Jun Jun} and Beibei Ren",

year = "2015",

month = mar,

day = "2",

doi = "10.1109/WCICA.2014.7052828",

language = "English",

series = "Proceedings of the World Congress on Intelligent Control and Automation (WCICA)",

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

number = "March",

pages = "856--860",

booktitle = "Proceeding of the 11th World Congress on Intelligent Control and Automation, WCICA 2014",

edition = "March",

note = "2014 11th World Congress on Intelligent Control and Automation, WCICA 2014 ; Conference date: 29-06-2014 Through 04-07-2014",

}

Wang, JM, Wang, LL, Liu, JJ & Ren, B 2015, Stabilization of a cascade system of ODE-PDE subject to boundary control matched disturbance. in Proceeding of the 11th World Congress on Intelligent Control and Automation, WCICA 2014. March edn, 7052828, Proceedings of the World Congress on Intelligent Control and Automation (WCICA), no. March, vol. 2015-March, Institute of Electrical and Electronics Engineers Inc., pp. 856-860, 2014 11th World Congress on Intelligent Control and Automation, WCICA 2014, Shenyang, China, 06/29/14. https://doi.org/10.1109/WCICA.2014.7052828

Stabilization of a cascade system of ODE-PDE subject to boundary control matched disturbance. / Wang, Jun Min; Wang, Li Li; Liu, Jun Jun et al.
Proceeding of the 11th World Congress on Intelligent Control and Automation, WCICA 2014. March. ed. Institute of Electrical and Electronics Engineers Inc., 2015. p. 856-860 7052828 (Proceedings of the World Congress on Intelligent Control and Automation (WCICA); Vol. 2015-March, No. March).

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

TY - GEN

T1 - Stabilization of a cascade system of ODE-PDE subject to boundary control matched disturbance

AU - Wang, Jun Min

AU - Wang, Li Li

AU - Liu, Jun Jun

AU - Ren, Beibei

PY - 2015/3/2

Y1 - 2015/3/2

N2 - In this paper, we are concerned with the boundary feedback stabilization of a cascade system of ODE-PDE with the external disturbance flowing the control end, where the PDE is described by a heat equation with Dirichlet interconnection. We use the sliding mode control (SMC) to deal with the disturbance. By the SMC approach, the disturbance is supposed to be bounded only. The existence and uniqueness of the solution for the closed-loop via SMC are proved, and the monotonicity of the 'reaching condition' is presented without the differentiation of the sliding mode function, for which it may not always exist for the weak solution of the closed-loop system.

AB - In this paper, we are concerned with the boundary feedback stabilization of a cascade system of ODE-PDE with the external disturbance flowing the control end, where the PDE is described by a heat equation with Dirichlet interconnection. We use the sliding mode control (SMC) to deal with the disturbance. By the SMC approach, the disturbance is supposed to be bounded only. The existence and uniqueness of the solution for the closed-loop via SMC are proved, and the monotonicity of the 'reaching condition' is presented without the differentiation of the sliding mode function, for which it may not always exist for the weak solution of the closed-loop system.

KW - Backstepping

KW - Boundary control

KW - Cascade systems

KW - Disturbance rejection

KW - Sliding mode control

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DO - 10.1109/WCICA.2014.7052828

M3 - Conference contribution

T3 - Proceedings of the World Congress on Intelligent Control and Automation (WCICA)

SP - 856

EP - 860

BT - Proceeding of the 11th World Congress on Intelligent Control and Automation, WCICA 2014

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2014 11th World Congress on Intelligent Control and Automation, WCICA 2014

Y2 - 29 June 2014 through 4 July 2014

ER -

Wang JM, Wang LL, Liu JJ, Ren B. Stabilization of a cascade system of ODE-PDE subject to boundary control matched disturbance. In Proceeding of the 11th World Congress on Intelligent Control and Automation, WCICA 2014. March ed. Institute of Electrical and Electronics Engineers Inc. 2015. p. 856-860. 7052828. (Proceedings of the World Congress on Intelligent Control and Automation (WCICA); March). doi: 10.1109/WCICA.2014.7052828

Stabilization of a cascade system of ODE-PDE subject to boundary control matched disturbance

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