Navier-Stokes系统降维模型中线性反馈控制的分析与逼近

Analysis and approximation of linear feedback control in the reduced modeling for Navier-Stokes flows

讨论了Navier-Stokes系统降维模型的线性反馈控制问题.首先介绍了特征正交分解方法(proper orthogonal decomposition,POD),然后利用该方法建立了Navier-Stokes系统反馈控制问题的降维模型,最后运用Ritz-Galerkin方法估计了线性反馈控制问题的降维模型解与有限元解之间的误差,并给出了计算降维模型解和速度跟踪问题的算法.

This paper discusses the linear feedback control of Navier-Stokes flows in a reduced-order modeling.Firstly,we introduce the proper orthogonal decomposition method.And then,use the method to establish a reduced-order modeling of the Navier-Stokes flows feedback control problem.Finally,we estimate the error between the finite element solution and the reduced-order modeling solution of the linear feedback control problem with the Ritz-Galerkin method,and propose algorithms for calculating the solution of reduced order modeling and velocity tracking problem.