  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.
