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

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.