  The Tokamak device is the most promising candidate for producing sustainable
electric power by nuclear fusion. It is a torus-shaped device that confines
plasma by a strong magnetic field. The development, design and control of the
design has been an important area of research, and a significant target is to
effectively confine the extremely hot plasma inside its hollow torus-shaped
body without touching its boundary for a prolonged period of time. In an
attempt to control a Tokamak device, this paper investigates an optimal control
problem for an incompressible, viscous, electrically conducting MHD fluid
confined in a closed toroidal region in the presence of an applied current. The
objective functional for the optimal control problem are subject to set of
constraint equations, Navier-Stokes and Maxwell equations. We target the
transient control of guiding the plasma to a desired flow at a particular short
time instant, where it is expected that the flow had been designed offline to
be the desired one from the point of view of steady state operation.
