SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 3, Page 1609-1632, January 2020.
The problems of (i) maximizing or minimizing Lagrangian mixing in fluids via the introduction of a spatiotemporally varying control velocity and (ii) globally controlling the finite-time location of trajectories beginning at all initial conditions in a chaotic system are considered. A particular form of solution to these is designed which uses a new methodology for computing a spatiotemporally dependent optimal control. An $L^2$-error norm for trajectory locations over a finite-time horizon is combined with a penalty energy norm for the control velocity in defining the global cost function. A computational algorithm for cost minimization is developed, and theoretical results on global error and cost presented. Numerical simulations (using velocities which are specified, and obtained as data from computational fluid dynamics simulations) are used to demonstrate the efficacy and validity of the approach in determining the required spatiotemporally defined control velocity.

中文翻译：

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通过时空有限时间全局最优控制轨迹

SIAM应用动力系统杂志，第19卷第3期，第1609-1632页，2020年1月。
考虑了以下问题：（i）通过引入时空变化的控制速度来最大化或最小化流体中的拉格朗日混合，以及（ii）全面控制从混沌系统中所有初始条件开始的轨迹的有限时间位置的问题。设计了这些解决方案的一种特殊形式，该解决方案使用一种新方法来计算时空相关的最优控制。在定义全局成本函数时，将有限时间范围内的轨迹位置的$ L ^ 2 $误差范数与控制速度的惩罚能量范数组合在一起。提出了一种用于成本最小化的计算算法，并给出了关于全局误差和成本的理论结果。数值模拟（使用指定的速度，