In this work, we present a new optimal control approach to fluid-structure interaction parameter estimation problems. The goal is to obtain the desired deformation by controlling the solid material properties, such as the Young modulus. We consider a stationary monolithic FSI problem where solid and liquid forces at the interface are automatically balanced. We consider inequality constraints in order to bound the Young modulus control admissible set. For the optimization, we adopt the Lagrange multiplier method with adjoint variables and obtain the optimality system which minimizes the augmented Lagrangian functional. We implement a projected gradient-based algorithm in a multigrid finite element code suitable for the study of large solid displacements. In order to support the proposed approach, we perform numerical tests with different objectives and control constraints.

在这项工作中，我们提出了一种新的最优控制方法来解决流固耦合参数估计问题。目的是通过控制诸如杨氏模量的固体材料特性来获得所需的变形。我们考虑一个固定的整体式FSI问题，其中界面处的固体和液体力会自动平衡。为了限制杨氏模量控制的可容许集合，我们考虑了不等式约束。为了进行优化，我们采用带有伴随变量的拉格朗日乘数法，并获得了使扩展的拉格朗日函数最小化的最优系统。我们在适用于大固体位移研究的多网格有限元代码中实现了基于投影的投影算法。为了支持提议的方法，