  In this article, we study the strong well-posedness, stability and optimal
control of an incompressible magneto-viscoelastic fluid model in two
dimensions. The model consists of an incompressible Navier--Stokes equation for
the velocity field, an evolution equation for the deformation tensor, and a
gradient flow equation for the magnetization vector. First, we prove that the
model under consideration posseses a global strong solution in a suitable
functional framework. Second, we derive stability estimates with respect to an
external magnetic field. Based on the stability estimates we use the external
magnetic field as the control to minimize a cost functional of tracking-type.
We prove existence of an optimal control and derive first-order necessary
optimality conditions. Finally, we consider a second optimal control problem,
where the external magnetic field, which represents the control, is generated
by a finite number of fixed magnetic field coils.
