In this article, we formulate a monolithic optimal control method for general time-dependent Fluid-Structure Interaction (FSI) systems with large solid deformation. We consider a displacement-tracking type of objective with a constraint of the solid velocity, tackle the time-dependent control problems by a piecewise-in-time control, cope with large solid displacement using a one-velocity fictitious domain method, and solve the fully-coupled FSI and the corresponding adjoint equations in a monolithic manner. We implement the proposed method in the open-source software package FreeFEM++ and assess it by three numerical experiments, in the aspects of stability of the numerical scheme for different regularisation parameters, and efficiency of reducing the objective function with control of the solid velocity.

中文翻译：

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大固体变形流固耦合问题的整体单速场最优控制公式

在本文中，我们为具有大固体变形的一般瞬态流固耦合 (FSI) 系统制定了整体最优控制方法。我们考虑具有固体速度约束的位移跟踪类型的目标，通过分段时间控制解决依赖于时间的控制问题，使用单速度虚拟域方法处理大固体位移，并解决以整体方式完全耦合 FSI 和相应的伴随方程。我们在开源软件包 FreeFEM++ 中实现了所提出的方法，并通过三个数值实验对其进行了评估，在不同正则化参数的数值方案的稳定性以及通过控制固体速度降低目标函数的效率方面。