SIAM Journal on Control and Optimization, Volume 58, Issue 6, Page 3658-3683, January 2020.
This work is concerned with the necessary conditions of optimality for a minimal time control problem $(P)$ related to the linearized Navier--Stokes periodic flow in a 2D-channel, subject to a boundary input which acts on the transversal component of the velocity. The objective in this problem is reaching the laminar regime in minimum time and preserving it after this time. The determination of the necessary conditions of optimality relies on the analysis of intermediate minimal time control problems $(P_{k})$ for the Fourier modes $``k''$ associated to the Navier--Stokes equations and on the proof of the maximum principle for them. Also it is found that one can construct, on the basis of the optimal controllers of problems $(P_{k}),$ a small time, called here quasi-minimal, and a boundary controller which realizes the required objective in $(P).$

中文翻译：

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二维通道中Navier-Stokes周期流的最短时间精确控制

SIAM控制与优化杂志，第58卷，第6期，第3658-3683页，2020年1月。
这项工作涉及与线性化Navier-Stokes 2D通道中的周期性流有关的最小时间控制问题$（P）$的最优性的必要条件，该条件取决于边界输入，该输入作用于对象的横向分量。速度。这个问题的目的是在最短的时间内达到层流状态，并在此时间后保留它。最优性必要条件的确定取决于对与Navier-Stokes方程相关的傅立叶模式$``k''$的中间最小时间控制问题$（P_ {k}）$的分析他们的最大原则。还发现，根据问题的最优控制器$（P_ {k}），可以构造一个小的时间，这里称为准最小，