二维非稳态对流扩散边界控制问题的简化算法
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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.
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.
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.
引文
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[2]胡健伟,汤怀民.微分方程数值方法[M].北京:科学出版社,2007.
[3]MUNYAKAZI J B.A uniformly convergent non-standard finite difference scheme for a system of con-vection diffusion equations[J].Computational&Applied Mathematics,2015,34(3):1153-1165.
[4]EGGER H,SCHBERL J.A hybrid mixed discontinuous Galerkin finite-element method for convection-diffusion problems[J].Ima Journal of Numerical Analysis,2018,30(4):1206-1234.
[5]罗振东,王瑞文,陈静,等.非定常的Navier Stokes方程基于特征正交分解的差分格式[J].中国科学:,2007,37(6):709-718.
[6]LENTH R V.Least-squares means:the R package lsmeans[J].Journal of Statistical Software,2016,69(1):1-33.
[7]LI M,CHRISTOFIDES P D.Optimal control of diffusion convection-reaction processes using reduced order models.Computers&Chemical Engineering,2008,32(9):2123-2135.
[8]DERKSEN H.On the Nuclear norm and the singular value decomposition of tensors[J].Foundations of Computational Mathematics,2016,16(3):779-811.