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Volume 6, Issue 1
Distributed Control of the Stochastic Burgers Equation with Random Input Data

Hyung-Chun Lee & Yun Nam

DOI: 10.4208/eajam.180615.080116a

East Asian J. Appl. Math., 6 (2016), pp. 89-108.

Published online: 2018-02

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  • Abstract

We discuss a control problem involving a stochastic Burgers equation with a random diffusion coefficient. Numerical schemes are developed, involving the finite element method for the spatial discretisation and the sparse grid stochastic collocation method in the random parameter space. We also use these schemes to compute closed-loop suboptimal state feedback control. Several numerical experiments are performed, to demonstrate the efficiency and plausibility of our approximation methods for the stochastic Burgers equation and the related control problem.

  • Keywords

Finite element method, feedback control, stochastic Burgers equation, sparse grid collocation.

  • AMS Subject Headings

49J20, 76D05, 49B22

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-6-89, author = {Hyung-Chun Lee and Yun Nam}, title = {Distributed Control of the Stochastic Burgers Equation with Random Input Data}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {6}, number = {1}, pages = {89--108}, abstract = {

We discuss a control problem involving a stochastic Burgers equation with a random diffusion coefficient. Numerical schemes are developed, involving the finite element method for the spatial discretisation and the sparse grid stochastic collocation method in the random parameter space. We also use these schemes to compute closed-loop suboptimal state feedback control. Several numerical experiments are performed, to demonstrate the efficiency and plausibility of our approximation methods for the stochastic Burgers equation and the related control problem.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.180615.080116a}, url = {http://global-sci.org/intro/article_detail/eajam/10916.html} }
TY - JOUR T1 - Distributed Control of the Stochastic Burgers Equation with Random Input Data AU - Hyung-Chun Lee & Yun Nam JO - East Asian Journal on Applied Mathematics VL - 1 SP - 89 EP - 108 PY - 2018 DA - 2018/02 SN - 6 DO - http://doi.org/10.4208/eajam.180615.080116a UR - https://global-sci.org/intro/article_detail/eajam/10916.html KW - Finite element method, feedback control, stochastic Burgers equation, sparse grid collocation. AB -

We discuss a control problem involving a stochastic Burgers equation with a random diffusion coefficient. Numerical schemes are developed, involving the finite element method for the spatial discretisation and the sparse grid stochastic collocation method in the random parameter space. We also use these schemes to compute closed-loop suboptimal state feedback control. Several numerical experiments are performed, to demonstrate the efficiency and plausibility of our approximation methods for the stochastic Burgers equation and the related control problem.

Hyung-Chun Lee and Yun Nam. (2018). Distributed Control of the Stochastic Burgers Equation with Random Input Data. East Asian Journal on Applied Mathematics. 6 (1). 89-108. doi:10.4208/eajam.180615.080116a
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