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The Youngnam Mathematical Society (영남수학회)
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REDUCED-ORDER BASED DISTRIBUTED FEEDBACK CONTROL OF THE BENJAMIN-BONA-MAHONY-BURGERS EQUATION

  • Jia, Li-Jiao (Department of Mathematics, Yanbian University) ;
  • Nam, Yun (Department of Mathematics, Ajou University) ;
  • Piao, Guang-Ri (Department of Mathematics, Yanbian University)
  • Received : 2018.07.03
  • Accepted : 2018.09.13
  • Published : 2018.09.30
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Abstract

In this paper, we discuss a reduced-order modeling for the Benjamin-Bona-Mahony-Burgers (BBMB) equation and its application to a distributed feedback control problem through the centroidal Voronoi tessellation (CVT). Spatial distcritization to the BBMB equation is based on the finite element method (FEM) using B-spline functions. To determine the basis elements for the approximating subspaces, we elucidate the CVT approaches to reduced-order bases with snapshots. For the purpose of comparison, a brief review of the proper orthogonal decomposition (POD) is provided and some numerical experiments implemented including full-order approximation, CVT based model, and POD based model. In the end, we apply CVT reduced-order modeling technique to a feedback control problem for the BBMB equation.

Keywords

References

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