Optimal Control of Heat Transfer in Unsteady Stokes Flows
Optimal Control of Heat Transfer in Unsteady Stokes Flows
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DOI：
10.1109/cdc.2018.8618869
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发表时间：
2018-12
期刊：
影响因子：
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通讯作者：
Weiwei Hu;O. San
中科院分区：
文献类型：
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作者：
Weiwei Hu;O. San
本文建立了一个严格的数学框架来解决非定常斯托克斯流传热的最优控制设计。我们特别关注通过控制冷流体流动的速度来增强两种流体之间的对流冷却问题，其中将研究内部和边界控制。这本质上导致了双线性控制问题。利用变分不等式给出了最优控制存在性的严格证明，并导出了最优性的一阶必要条件。最后，我们证明了当控制权足够大时，最优控制器的唯一性是可以得到的。
This paper is concerned with establishing a rigorous mathematical framework to address optimal control designs for heat transfer in unsteady Stokes flows. In particular, we focus on the problem of enhancing convection-cooling between two fluids via controlling the velocity of the cold fluid flow, where both internal and boundary controls will be investigated. This essentially leads to a bilinear control problem. We present a rigorous proof of the existence of an optimal control and derive the first-order necessary conditions for optimality by using a variational inequality. Finally, we show that the uniqueness of the optimal controller can be obtained if the control weight is sufficiently large.