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Computational and Applied Mathematics Journal

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A Reduced Scheme Based on POD for a Convection-Diffusion Boundary Control Problem with Control/State Constraints

Computational and Applied Mathematics Journal
Vol.4 , No. 4, Publication Date: Jan. 19, 2019, Page: 57-64

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Authors

[1]	Guoping Zhang, College of Mathematics and Statistics, Guizhou University, Guiyang, P.R. China.
[2]	Xianbing Luo, College of Mathematics and Statistics, Guizhou University, Guiyang, P.R. China.

Abstract

To solve a problem of high real--time performance and large computational complexity in two--dimensional convection--diffusion boundary control problem with constraints, an optimal real--time control method based on reduced order model with constraints is proposed. Using proper orthogonal decomposition (POD) of snapshot, we first obtain a reduced finite difference scheme. Then, a quadratic programming method with constraints sing-step rolling optimization algorithm (CSROA) is adopted and verified with improved saturated linear quadratic regulator (ISLQR) controller. Finally, to verify the validity and accuracy of the proposed method, numerical simulations are presented.

Keywords

Convection-Diffusion, Boundary Control, POD

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