Sliding mode control to the stabilization of a linear 2×2 hyperbolic system with boundary input disturbance

Shuxia Tang; Miroslav Krstic

doi:10.1109/ACC.2014.6858635

Sliding mode control to the stabilization of a linear 2×2 hyperbolic system with boundary input disturbance

Shuxia Tang, Miroslav Krstic

Mechanical Engineering

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

28 Scopus citations

Abstract

In this paper, sliding mode control approach is used to stabilize a 2×2 system of first-order linear hyperbolic PDEs subject to boundary input disturbance. Disturbance rejection is achieved, and with the designed first-order sliding mode controller, the resulting closed-loop system admits a unique (mild) solution without chattering. Convergence to the chosen infinite-dimensional sliding surface of state trajectories takes place in a finite time. Then on the sliding surface, the system is exponentially stable with a decay rate depending on the spatially varying system coefficients. A simulation example is presented to illustrate the effectiveness and performance of sliding mode control method.

Original language	English
Title of host publication	2014 American Control Conference, ACC 2014
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1027-1032
Number of pages	6
ISBN (Print)	9781479932726
DOIs	https://doi.org/10.1109/ACC.2014.6858635
State	Published - 2014
Event	2014 American Control Conference, ACC 2014 - Portland, OR, United States Duration: Jun 4 2014 → Jun 6 2014

Publication series

Name	Proceedings of the American Control Conference
ISSN (Print)	0743-1619

Conference

Conference	2014 American Control Conference, ACC 2014
Country/Territory	United States
City	Portland, OR
Period	06/4/14 → 06/6/14

Keywords

Backstepping
Disturbance rejection
First-order sliding mode control
Linear 2×2 hyperbolic system

Access to Document

10.1109/ACC.2014.6858635

Cite this

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title = "Sliding mode control to the stabilization of a linear 2×2 hyperbolic system with boundary input disturbance",

abstract = "In this paper, sliding mode control approach is used to stabilize a 2×2 system of first-order linear hyperbolic PDEs subject to boundary input disturbance. Disturbance rejection is achieved, and with the designed first-order sliding mode controller, the resulting closed-loop system admits a unique (mild) solution without chattering. Convergence to the chosen infinite-dimensional sliding surface of state trajectories takes place in a finite time. Then on the sliding surface, the system is exponentially stable with a decay rate depending on the spatially varying system coefficients. A simulation example is presented to illustrate the effectiveness and performance of sliding mode control method.",

keywords = "Backstepping, Disturbance rejection, First-order sliding mode control, Linear 2×2 hyperbolic system",

author = "Shuxia Tang and Miroslav Krstic",

year = "2014",

doi = "10.1109/ACC.2014.6858635",

language = "English",

isbn = "9781479932726",

series = "Proceedings of the American Control Conference",

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

pages = "1027--1032",

booktitle = "2014 American Control Conference, ACC 2014",

note = "2014 American Control Conference, ACC 2014 ; Conference date: 04-06-2014 Through 06-06-2014",

}

Tang, S & Krstic, M 2014, Sliding mode control to the stabilization of a linear 2×2 hyperbolic system with boundary input disturbance. in 2014 American Control Conference, ACC 2014., 6858635, Proceedings of the American Control Conference, Institute of Electrical and Electronics Engineers Inc., pp. 1027-1032, 2014 American Control Conference, ACC 2014, Portland, OR, United States, 06/4/14. https://doi.org/10.1109/ACC.2014.6858635

Sliding mode control to the stabilization of a linear 2×2 hyperbolic system with boundary input disturbance. / Tang, Shuxia; Krstic, Miroslav.
2014 American Control Conference, ACC 2014. Institute of Electrical and Electronics Engineers Inc., 2014. p. 1027-1032 6858635 (Proceedings of the American Control Conference).

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

TY - GEN

T1 - Sliding mode control to the stabilization of a linear 2×2 hyperbolic system with boundary input disturbance

AU - Tang, Shuxia

AU - Krstic, Miroslav

PY - 2014

Y1 - 2014

N2 - In this paper, sliding mode control approach is used to stabilize a 2×2 system of first-order linear hyperbolic PDEs subject to boundary input disturbance. Disturbance rejection is achieved, and with the designed first-order sliding mode controller, the resulting closed-loop system admits a unique (mild) solution without chattering. Convergence to the chosen infinite-dimensional sliding surface of state trajectories takes place in a finite time. Then on the sliding surface, the system is exponentially stable with a decay rate depending on the spatially varying system coefficients. A simulation example is presented to illustrate the effectiveness and performance of sliding mode control method.

AB - In this paper, sliding mode control approach is used to stabilize a 2×2 system of first-order linear hyperbolic PDEs subject to boundary input disturbance. Disturbance rejection is achieved, and with the designed first-order sliding mode controller, the resulting closed-loop system admits a unique (mild) solution without chattering. Convergence to the chosen infinite-dimensional sliding surface of state trajectories takes place in a finite time. Then on the sliding surface, the system is exponentially stable with a decay rate depending on the spatially varying system coefficients. A simulation example is presented to illustrate the effectiveness and performance of sliding mode control method.

KW - Backstepping

KW - Disturbance rejection

KW - First-order sliding mode control

KW - Linear 2×2 hyperbolic system

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U2 - 10.1109/ACC.2014.6858635

DO - 10.1109/ACC.2014.6858635

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SN - 9781479932726

T3 - Proceedings of the American Control Conference

SP - 1027

EP - 1032

BT - 2014 American Control Conference, ACC 2014

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2014 American Control Conference, ACC 2014

Y2 - 4 June 2014 through 6 June 2014

ER -

Sliding mode control to the stabilization of a linear 2×2 hyperbolic system with boundary input disturbance

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Keywords

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