二维非稳态对流扩散边界控制问题的简化算法
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引用本文:张国平, 罗贤兵.二维非稳态对流扩散边界控制问题的简化算法[J].经济数学,2019,(1):91-95
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作者单位
张国平, 罗贤兵 (贵州大学 数学与统计学院, 贵州 贵阳 550025) 
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 Two-Dimensional Unsteady Convective-Diffusion Boundary Control Problems
Abstract:Boundary control of two-dimensional unsteady convection diffusion is a large-scale optimization problem, and an approach was 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 were 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 the proposed method.
keywords:convection-diffusion boundary control problem  the Proper Orthogonal Decomposition (POD)  singular value decomposition  dimensionality reduction model
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