Sliding mode dirichlet boundary stabilization of uncertain parabolic pde systems with spatially varying coefficients

Meng Bi Cheng; Verica Radisavljevic; Tsung Lin Tsai; Wu Chung Su

doi:10.1109/ACC.2010.5530940

Sliding mode dirichlet boundary stabilization of uncertain parabolic pde systems with spatially varying coefficients

Meng Bi Cheng
, Verica Radisavljevic
, Tsung Lin Tsai
, Wu Chung Su

National Chung Hsing University
California State University Los Angeles

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

Abstract

We consider the robust boundary stabilization problem of an unstable parabolic partial differential equation (PDE) system with uncertainties entering from both the spatially-dependent parameters and from the boundary conditions. The parabolic PDE is transformed through the Volterra integral into a damped heat equation with uncertainties, which contains the matched part (the boundary disturbance) and the mismatched part (the parameter variations). In this new coordinates, an infinite-dimensional sliding manifold that ensures system stability is constructed. For the sliding mode boundary control law to satisfy the reaching condition, an adaptive switching gain is used to cope with the above uncertainties, whose bound is unknown.

Original language	English
Title of host publication	Proceedings of the 2010 American Control Conference, ACC 2010
Publisher	IEEE Computer Society
Pages	3341-3346
Number of pages	6
ISBN (Print)	9781424474264
DOIs	https://doi.org/10.1109/ACC.2010.5530940
State	Published - 2010
Externally published	Yes

Publication series

Name	Proceedings of the 2010 American Control Conference, ACC 2010

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10.1109/ACC.2010.5530940

Cite this

Cheng, M. B., Radisavljevic, V., Tsai, T. L., & Su, W. C. (2010). Sliding mode dirichlet boundary stabilization of uncertain parabolic pde systems with spatially varying coefficients. In Proceedings of the 2010 American Control Conference, ACC 2010 (pp. 3341-3346). Article 5530940 (Proceedings of the 2010 American Control Conference, ACC 2010). IEEE Computer Society. https://doi.org/10.1109/ACC.2010.5530940

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title = "Sliding mode dirichlet boundary stabilization of uncertain parabolic pde systems with spatially varying coefficients",

abstract = "We consider the robust boundary stabilization problem of an unstable parabolic partial differential equation (PDE) system with uncertainties entering from both the spatially-dependent parameters and from the boundary conditions. The parabolic PDE is transformed through the Volterra integral into a damped heat equation with uncertainties, which contains the matched part (the boundary disturbance) and the mismatched part (the parameter variations). In this new coordinates, an infinite-dimensional sliding manifold that ensures system stability is constructed. For the sliding mode boundary control law to satisfy the reaching condition, an adaptive switching gain is used to cope with the above uncertainties, whose bound is unknown.",

author = "Cheng, \{Meng Bi\} and Verica Radisavljevic and Tsai, \{Tsung Lin\} and Su, \{Wu Chung\}",

year = "2010",

doi = "10.1109/ACC.2010.5530940",

language = "English",

isbn = "9781424474264",

series = "Proceedings of the 2010 American Control Conference, ACC 2010",

publisher = "IEEE Computer Society",

pages = "3341--3346",

booktitle = "Proceedings of the 2010 American Control Conference, ACC 2010",

address = "United States",

}

Cheng, MB, Radisavljevic, V, Tsai, TL & Su, WC 2010, Sliding mode dirichlet boundary stabilization of uncertain parabolic pde systems with spatially varying coefficients. in Proceedings of the 2010 American Control Conference, ACC 2010., 5530940, Proceedings of the 2010 American Control Conference, ACC 2010, IEEE Computer Society, pp. 3341-3346. https://doi.org/10.1109/ACC.2010.5530940

Sliding mode dirichlet boundary stabilization of uncertain parabolic pde systems with spatially varying coefficients. / Cheng, Meng Bi; Radisavljevic, Verica; Tsai, Tsung Lin et al.
Proceedings of the 2010 American Control Conference, ACC 2010. IEEE Computer Society, 2010. p. 3341-3346 5530940 (Proceedings of the 2010 American Control Conference, ACC 2010).

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

TY - GEN

T1 - Sliding mode dirichlet boundary stabilization of uncertain parabolic pde systems with spatially varying coefficients

AU - Cheng, Meng Bi

AU - Radisavljevic, Verica

AU - Tsai, Tsung Lin

AU - Su, Wu Chung

PY - 2010

Y1 - 2010

N2 - We consider the robust boundary stabilization problem of an unstable parabolic partial differential equation (PDE) system with uncertainties entering from both the spatially-dependent parameters and from the boundary conditions. The parabolic PDE is transformed through the Volterra integral into a damped heat equation with uncertainties, which contains the matched part (the boundary disturbance) and the mismatched part (the parameter variations). In this new coordinates, an infinite-dimensional sliding manifold that ensures system stability is constructed. For the sliding mode boundary control law to satisfy the reaching condition, an adaptive switching gain is used to cope with the above uncertainties, whose bound is unknown.

AB - We consider the robust boundary stabilization problem of an unstable parabolic partial differential equation (PDE) system with uncertainties entering from both the spatially-dependent parameters and from the boundary conditions. The parabolic PDE is transformed through the Volterra integral into a damped heat equation with uncertainties, which contains the matched part (the boundary disturbance) and the mismatched part (the parameter variations). In this new coordinates, an infinite-dimensional sliding manifold that ensures system stability is constructed. For the sliding mode boundary control law to satisfy the reaching condition, an adaptive switching gain is used to cope with the above uncertainties, whose bound is unknown.

UR - https://www.scopus.com/pages/publications/77957802893

U2 - 10.1109/ACC.2010.5530940

DO - 10.1109/ACC.2010.5530940

M3 - Conference contribution

AN - SCOPUS:77957802893

SN - 9781424474264

T3 - Proceedings of the 2010 American Control Conference, ACC 2010

SP - 3341

EP - 3346

BT - Proceedings of the 2010 American Control Conference, ACC 2010

PB - IEEE Computer Society

ER -

Cheng MB, Radisavljevic V, Tsai TL, Su WC. Sliding mode dirichlet boundary stabilization of uncertain parabolic pde systems with spatially varying coefficients. In Proceedings of the 2010 American Control Conference, ACC 2010. IEEE Computer Society. 2010. p. 3341-3346. 5530940. (Proceedings of the 2010 American Control Conference, ACC 2010). doi: 10.1109/ACC.2010.5530940

Sliding mode dirichlet boundary stabilization of uncertain parabolic pde systems with spatially varying coefficients

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