对流扩散边界控制问题的简化算法
投稿时间:2018-10-25  修订日期:2018-10-25  点此下载全文
引用本文:
摘要点击次数: 315
全文下载次数: 0
作者单位邮编
张国平 贵州大学数学与统计学院 550025
基金项目:国家自然科学基金项目(面上项目,重点项目,重大项目)
中文摘要:针对二维非稳态对流扩散边界控制问题计算量大的问题, 提出了基于降阶模型的最优实时控制方法. 利用POD(the Proper Orthogonal Decomposition)和奇异值分解以及Galerkin投影方法得到了具有高精度离散形式的状态空间降阶模型. 在所得的降阶状态空间模型中, 利用离散时间线性二次调节器方法设计出了最优控制器. 对流-扩散过程的控制模拟结果说明了所提方法的有效性和准确性.
中文关键词:对流扩散边界控制问题  特征正交分解(POD)  奇异值分解  降维模型.
 
A reduced algorithm for convective- diffusion boundary control problems
Abstract:Boundary control of two-dimensional unsteady convection diffusion is a large-scale optimization problem, an approach is presented for optimal control based on reduced-order model, which was derived from a discrete-time low-order state-space model with high accuracy by using POD(the Proper Orthogonal Decomposition), singular value decomposition (SVD)and Galerkin projection. Optimal controllers are designed based on the low-order state-space models using discrete-time linear quadratic regulator (LQR) techniques. The controlling simulation results in the convection-diffusion process illustrate the effectiveness and accuracy of proposed method.
keywords:Convection-diffusion boundary control problem  the Proper Orthogonal Decomposition (POD)  singular value decomposition  dimensionality reduction model.
查看全文   查看/发表评论   下载pdf阅读器