POD-Based Economic Optimal Control of Heat-Convection Phenomena
POD-Based Economic Optimal Control of Heat-Convection Phenomena
复制标题
基于 POD 的热对流现象经济优化控制
DOI：
10.1007/978-3-030-01959-4_4
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
S. Volkwein
中科院分区：
文献类型：
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作者：
L. Mechelli;S. Volkwein
在节能建筑运行的设置，最优边界控制问题所管辖的热方程与对流项被认为是双边控制和状态约束。其目的是以尽可能少的加热成本将温度保持在规定的范围内。为了获得规则的拉格朗日乘子的状态约束的Lavrentiev正则化。正则化的最优控制问题是解决的原始-对偶有效集策略（PDASS），它可以被解释为一个半光滑牛顿法，因此，具有超线性收敛速度。为了加快PDASS的降阶方法的基础上适当的正交分解（POD）。一个后验误差分析，确保计算（次优）POD解决方案是足够准确的。数值试验表明了该策略的有效性。
In the setting of energy efficient building operation, an optimal boundary control problem governed by the heat equation with a convection term is considered together with bilateral control and state constraints. The aim is to keep the temperature in a prescribed range with the least possible heating cost. In order to gain regular Lagrange multipliers a Lavrentiev regularization for the state constraints is utilized. The regularized optimal control problem is solved by a primal-dual active set strategy (PDASS) which can be interpreted as a semismooth Newton method and, therefore, has a superlinear rate of convergence. To speed up the PDASS a reduced-order approach based on proper orthogonal decomposition (POD) is applied. An a-posteriori error analysis ensures that the computed (suboptimal) POD solutions are sufficiently accurate. Numerical test illustrates the efficiency of the proposed strategy.
DOI：
10.2172/1577437
发表时间：
2019-03
期刊：
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影响因子：
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作者：
S. Balay;S. Abhyankar;M. Adams;Jed Brown;P. Brune;K. Buschelman;Lisandro Dalcin;A. Dener;
通讯作者：
S. Balay;S. Abhyankar;M. Adams;Jed Brown;P. Brune;K. Buschelman;Lisandro Dalcin;A. Dener;