An optimal control approach to a fluid-structure interaction parameter estimation problem with inequality constraints

•We study a new optimal control approach to FSI parameter estimation problems.•We study the steady monolithic FSI problem with Young modulus control.•We use a fictitious velocity field and balance adjoint forces as well.•We implemented a projected gradient based algorithm with bounded controls. 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.