Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
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REDUCED-ORDER APPROACH USING WEIGHTED CENTROIDAL VORONOI TESSELLATION

  • Piao, Guang-Ri (INSTITUTE OF MATHEMATICAL SCIENCES, EWHA WOMANS UNIV., DEPARTMENT OF MATHEMATICS, YANBIAN UNIVERSITY) ;
  • Lee, Hyung-Chen (DEPARTMENT OF MATHEMATICS, AJOU UNIVERSITY) ;
  • Lee, June-Yub (DEPARTMENT OF MATHEMATICS, EWHA WOMANS UNIVERSITY)
  • Received : 2009.11.06
  • Accepted : 2009.12.05
  • Published : 2009.12.25
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Abstract

In this article, we study a reduced-order modelling for distributed feedback control problem of the Burgers equations. Brief review of the centroidal Voronoi tessellation (CVT) are provided. A weighted (nonuniform density) CVT is introduced and low-order approximate solution and compensator-based control design of Burgers equation is discussed. Through weighted CVT (or CVT-nonuniform) method, obtained low-order basis is applied to low-order 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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