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Boundary Feedback Control of the Burgers Equations by a Reduced-Order Approach Using Centroidal Voronoi Tessellations

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Abstract

In this paper, we study a reduced-order modelling for boundary feedback control problem of Burgers equations. Brief review of the CVT (centroidal Voronoi tessellation) approaches to reduced-order basis are provided. In CVT-reduced order modelling, we start with a snapshot set just as is done in a SVD (Singular Value Decomposition)-based setting. A weighted (nonuniform density) CVT is introduced and low-order approximate solution and compensator-based control design of Burgers equation is discussed. Through CVT-nonuniform method, the low-order basis is obtained. Then this low-order basis is applied to low-order approximate solution and functional gains to design a low-order controller, and by using the low-order basis order of control modelling was reduced. Numerical experiments show that a solution of reduced-order controlled Burgers equation performs well in comparison with a solution of full order controlled Burgers equation.

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Authors and Affiliations

  1. Department of Mathematics, Ajou University, Suwon, 443-749, Korea

    Hyung-Chun Lee & Guang-Ri Piao

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  1. Hyung-Chun Lee
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  2. Guang-Ri Piao
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Correspondence to Hyung-Chun Lee.

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This work was supported by grant No. R01-2006-000-10472-0 from KOSEF.

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Lee, HC., Piao, GR. Boundary Feedback Control of the Burgers Equations by a Reduced-Order Approach Using Centroidal Voronoi Tessellations. J Sci Comput 43, 369–387 (2010). https://doi.org/10.1007/s10915-009-9310-4

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  • DOI: https://doi.org/10.1007/s10915-009-9310-4

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