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Volume 5, Issue 1
Distributed Feedback Control of the Benjamin-Bona-Mahony-Burgers Equation by a Reduced-Order Model

Guang-Ri Piao & Hyung-Chun Lee

East Asian J. Appl. Math., 5 (2015), pp. 61-74.

Published online: 2018-02

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  • Abstract

A reduced-order model for distributed feedback control of the Benjamin-Bona-Mahony-Burgers (BBMB) equation is discussed. To retain more information in our model, we first calculate the functional gain in the full-order case, and then invoke the proper orthogonal decomposition (POD) method to design a low-order controller and thereby reduce the order of the model. Numerical experiments demonstrate that a solution of the reduced-order model performs well in comparison with a solution for the full-order description.

  • AMS Subject Headings

49J20, 76D05, 49B22

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COPYRIGHT: © Global Science Press

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@Article{EAJAM-5-61, author = {Guang-Ri Piao and Hyung-Chun Lee}, title = {Distributed Feedback Control of the Benjamin-Bona-Mahony-Burgers Equation by a Reduced-Order Model}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {5}, number = {1}, pages = {61--74}, abstract = {

A reduced-order model for distributed feedback control of the Benjamin-Bona-Mahony-Burgers (BBMB) equation is discussed. To retain more information in our model, we first calculate the functional gain in the full-order case, and then invoke the proper orthogonal decomposition (POD) method to design a low-order controller and thereby reduce the order of the model. Numerical experiments demonstrate that a solution of the reduced-order model performs well in comparison with a solution for the full-order description.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.210214.061214a}, url = {http://global-sci.org/intro/article_detail/eajam/10779.html} }
TY - JOUR T1 - Distributed Feedback Control of the Benjamin-Bona-Mahony-Burgers Equation by a Reduced-Order Model AU - Guang-Ri Piao & Hyung-Chun Lee JO - East Asian Journal on Applied Mathematics VL - 1 SP - 61 EP - 74 PY - 2018 DA - 2018/02 SN - 5 DO - http://doi.org/10.4208/eajam.210214.061214a UR - https://global-sci.org/intro/article_detail/eajam/10779.html KW - B-spline finite element method, linear quadratic regulator, feedback control, reduce-dorder model, BBMB equation. AB -

A reduced-order model for distributed feedback control of the Benjamin-Bona-Mahony-Burgers (BBMB) equation is discussed. To retain more information in our model, we first calculate the functional gain in the full-order case, and then invoke the proper orthogonal decomposition (POD) method to design a low-order controller and thereby reduce the order of the model. Numerical experiments demonstrate that a solution of the reduced-order model performs well in comparison with a solution for the full-order description.

Guang-Ri Piao and Hyung-Chun Lee. (2018). Distributed Feedback Control of the Benjamin-Bona-Mahony-Burgers Equation by a Reduced-Order Model. East Asian Journal on Applied Mathematics. 5 (1). 61-74. doi:10.4208/eajam.210214.061214a
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